Operator algebras, free groups and other groups

de la Harpe, Pierre

Recent advances in operator algebras - Orléans, 1992, Astérisque, no. 232 (1995), pp. 121-153.

MR Zbl

@incollection{AST_1995__232__121_0,
     author = {de la Harpe, Pierre},
     title = {Operator algebras, free groups and other groups},
     booktitle = {Recent advances in operator algebras - Orl\'eans, 1992},
     series = {Ast\'erisque},
     pages = {121--153},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {232},
     year = {1995},
     zbl = {0846.46039},
     mrnumber = {1372530},
     language = {en},
     url = {http://archive.numdam.org/item/AST_1995__232__121_0/}
}

TY  - CHAP
AU  - de la Harpe, Pierre
TI  - Operator algebras, free groups and other groups
BT  - Recent advances in operator algebras - Orléans, 1992
AU  - Collectif
T3  - Astérisque
PY  - 1995
SP  - 121
EP  - 153
IS  - 232
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_1995__232__121_0/
LA  - en
ID  - AST_1995__232__121_0
ER  -

%0 Book Section
%A de la Harpe, Pierre
%T Operator algebras, free groups and other groups
%B Recent advances in operator algebras - Orléans, 1992
%A Collectif
%S Astérisque
%D 1995
%P 121-153
%N 232
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_1995__232__121_0/
%G en
%F AST_1995__232__121_0

de la Harpe, Pierre. Operator algebras, free groups and other groups, dans Recent advances in operator algebras - Orléans, 1992, Astérisque, no. 232 (1995), pp. 121-153. http://archive.numdam.org/item/AST_1995__232__121_0/

Bibliographie
Cité par

[Ake] C. A. Akemann, Operator Algebras Associated with Fuchsian Groups, Houston J. Math. 7 (1981), 295-301. | MR | Zbl

[ABH] J. Anderson, B. Blackadar and U. Haagerup, Minimal Projections in the Reduced Group $C^{*}$ -algebra of $ℤ_{n} ☆ ℤ_{m}$ , J. Operator Theory 26 (1991), 3-23. | MR | Zbl

[AkL] C. A. Akemann and Tan-Yu Lee, Some Simple $C^{*}$ -algebras Associated with Free Groups, Indiana Univ. Math. J. 29 (1980), 505-511. | DOI | MR | Zbl

[AkO] C. A. Akemann and P. A. Ostrand, Computing Norms in Group $C^{*}$ -algebras, Amer. J. Math. 98 (1976), 1015-1047. | DOI | MR | Zbl

[ASS] H. Araki, M. Smith and L. Smith, On the Homotopical Significance of the Type of von Neumann Algebra Factors, Commun. Math. Phys. 22 (1971), 71-88. | DOI | MR | Zbl

[Bas] H. Bass, Euler Characteristics and Characters of Discrete Groups, Inventiones Math. 35 (1976), 155-196. | DOI | EuDML | MR | Zbl

[BaC] P. Baum and A. Connes, $K$ -theory for Discrete Groups, Operator Algebras and Application, volume 1, edited by D.E. Evans and M. Takesaki, Cambridge Univ. Press (1988), 1-20. | Zbl

[Be1] E. Bédos, Simple $C^{*}$ -algebras and Discrete Groups, Math. Proc. Camb. Phil. Soc. 109 (1991), 521-537. | DOI | MR | Zbl

[Be2] E. Bédos, On the Uniqueness of the Trace on some Simple $C^{*}$ -algebras, J. Operator Theory (To appear). | MR | Zbl

[BdH] E. Bédos et P. De La Harpe, Moyennabilité intérieure des groupes : définitions et exemples, l'Enseignement math. 32 (1986), 139-157. | MR | Zbl

[Beh1] H. Behncke, Automorphisms of crossed products, Tôhoku Math. J. 21 (1969), 580-600. | DOI | MR | Zbl

[Beh2] H. Behncke, Generators of $W^{*}$ -algebras, Tôhoku Math. J. 22 (1970), 541-546. | DOI | MR | Zbl

[Beh3] H. Behncke, Generators of Finite $W^{*}$ -algebras, Tôhoku Math. J. 24 (1972), 401-408. | DOI | MR | Zbl

[BCH] M. Bekka, M. Cowling et P. De La Harpe, Some Groups whose Reduced $C^{*}$ -algebra is Simple, Preprint, New South Wales (January 1993). | Numdam | MR | Zbl

[BkH] M. Bekka et P. De La Harpe, Représentations d'un groupe faiblement équivalentes à la représentation régulière, Bull. Soc. Math. France (to appear). | EuDML | Numdam | MR | Zbl

[BeV] M. Bekka and A. Valette, Lattices in Semi-simple Lie Groups, and Multipliers of Group $C^{*}$ -algebras, These Proceedings.

[BeL] Y. Benoist and F. Labourie, Sur les difféomorphismes d'Anosov affines à feuilletages stable et instable différentiables, Inventiones Math. 111 (1993), 285-308. | DOI | EuDML | MR | Zbl

[BN1] F. Boca and V. Nitica, Combinatorial Properties of Groups and Simple $C^{*}$ -algebras with a Unique Trace, J. Operator Theory 20 (1988), 183-196. | MR | Zbl

[BN2] F. Boca and V. Nitica, Extensions of Groups and Simple $C^{*}$ -algebras, in "Linear Operators in Function Spaces (Timisoara 1988)", edited by H. Helson et al., Birkhäuser (1990), 123-130. | DOI | MR | Zbl

[Bo1] A. Borel, Density Properties for Certain Subgroups of Semisimple Lie Groups Without Compact Factors, Ann. of Math. 72 (1960), 179-188. | DOI | MR | Zbl

[Bo2] A. Borel, On Free Subgroups of Semi-Simple Groups, l'Enseignement math. 29 (1983), 151-164. | MR | Zbl

[Bou] N. Bourbaki, Algèbre, chapitres 4 à 7, Masson, 1981. | MR | Zbl

[Bro] L. G. Brown, Ext of Certain Free Product $C^{*}$ -algebras, J. Operator Theory 6 (1981), 135-141. | MR | Zbl

[BoP] M. Bozejko and M. A. Picardello, Weakly amenable groups and amalgamated products, Proc. Amer. Math. Soc. 117 (1993), 1039-1046. | DOI | MR | Zbl

[CaH] J. De Cannière and U. Haagerup, Multipliers of the Fourier Algebras of some Simple Lie Groups and their Discrete Subgroups, Amer. J. Math. 107 (1985),. 455-500. | DOI | MR | Zbl

[Cha] C. Champetier, Propriétés génériques des groupes de type fini, Thesis, Lyon (1991).

[ChM] B. Chandler and W. Magnus, The History of Combinatorial Group Theory : a Case Study in the History of Ideas, Springer, 1982. | MR | Zbl

[Cho] M. D. Choi, The Full $C^{*}$ -algebra of the Free Group on Two Generators, Pacific J. Math. 87 (1980), 41-48. | DOI | MR | Zbl

[Coh1] J. Cohen, $C^{*}$ -algebras without Idempotents, J. Functional Analysis 33 (1979), 211-216. | DOI | MR | Zbl

[Coh2] J. Cohen, Cogrowth and Amenability or Discrete Groups, J. Functional Analysis 48 (1982), 301-309. | DOI | MR | Zbl

[Co74] A. Connes, Almost Periodic States and Factors of Type III1, J. Functional Analysis 16 (1974), 415-445. | DOI | MR | Zbl

[Co75] A. Connes, Sur la classification des facteurs de type II, C.R. Acad. Sci. Paris 281, Série A (1975), 13-15. | MR | Zbl

[Co76] A. Connes, Classification of Injective Factors, Ann. of Math. 104 (1976), 73-115. | MR | Zbl

[C76b] A. Connes, On the Classification of von Neumann Algebras and their Automorphisms, Symposia Math. XX (1976), 378-435. | MR | Zbl

[Co78] A. Connes, On the Cohomology of Operator Algebras, J. Functional Analysis 28 (1978), 248-253. | DOI | MR | Zbl

[Co80] A. Connes, A factor of type $I I_{1}$ with countable fundamental group, J. Operator Theory 4 (1980), 151-153. | MR | Zbl

[Co86] A. Connes, Non-commutative Differential Geometry, Part I, The Chern Character in $K$ -homology, Part II, de Rham Homology and Non-commutative Algebra, Publ. Math. I.H.E.S. 62 (1986), 40-144. | EuDML | Numdam | Zbl

[Co90] A. Connes, Géométrie non commutative, InterEditions, 1990. | MR | Zbl

[Co93] A. Connes, Non Commutative Geometry, Preprint, IHES, 1993 (extended translation of [Co90]), and Academic Press, to appear. | Zbl

[CoJ] A. Connes and V. Jones, Property $T$ for von Neumann Algebras, Bull. London Math. Soc. 17 (1985), 57-62. | DOI | MR | Zbl

[CoM] A. Connes and H. Moscovici, Cyclic Cohomology, the Novikov Conjecture and Hyperbolic Groups, Topology 29 (1990), 345-388. | DOI | MR | Zbl

[Cw1] M. Cowling, The Kunze-Stein Phenomenon, Ann. of Math. 107 (1978), 209-234. | DOI | MR | Zbl

[Cw2] M. Cowling, Sur les coefficients des représentations unitaires des groupes de Lie simples, in "Analyse harmonique sur les groupes de Lie II (Séminaire Nancy-Strasbourg 1976-68)" edited by P. Eymard et al., Springer Lecture Notes in Math. 739 (1979), 132-178. | MR | Zbl

[Cw3] M. Cowling, Rigidity for Lattices in Semisimple Lie Groups : von Neumann Algebras and Ergodic Actions, Rend. Sem. Mat. Univers. Politecn. Torino 47 (1989), 1-37. | MR | Zbl

[CoH] M. Cowling and U. Haagerup, Completely Bounded Multipliers of the Fourier Algebra of a Simple Lie Group of Real Rank One, Inventiones Math. 96 (1989), 507-549. | DOI | EuDML | MR | Zbl

[CoH] M. Cowling, U. Haagerup and R. Howe, Almost $L^{2}$ Matrix Coefficients, J. reine angew. Math. 387 (1988), 97-110. | EuDML | MR | Zbl

[CoS] M. Cowling et T. Steger, The Irreducibility of Restrictions of Unitary Representations to Lattices, J. reine angew. Math. 420 (1991), 85-98. | EuDML | MR | Zbl

[CxM] H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups (4th edition), Springer, 1980. | MR | Zbl

[Cu1] J. Cuntz, The $K$ -groups for Free Products of $C^{*}$ -algebras, Proc. Symp. Pure Math. 38, Part I (1982), 81-84. | DOI | MR | Zbl

[Cu2] J. Cuntz, $K$ -theoretic amenability for discrete groups, J. reine Ang. Math. 344 (1983), 180-195. | EuDML | MR | Zbl

[DeS] P. Deligne and D. Sullivan, Division Algebras and the Hausdorff-Banach-Tarski Paradox, l'Enseignement math. 29 (1983), 145-150. | MR | Zbl

[Del] T. Delzant, Sous-groupes à deux générateurs des groupes hyperboliques, in "Group Theory from a Geometric Viewpoint (26 March - 6 April 1990, Trieste)", edited by E. Ghys et al., World Scientific (1991), 177-189. | MR | Zbl

[DC*] J. Dixmier, Les $C^{*}$ -algèbres et leurs représentations, Gauthier-Villars, 1969. | MR | Zbl

[Dy1] K. J. Dykema, Interpolated Free Group Factors, Pacific J. Math. (To appear). | MR | Zbl

[Dy2] K. J. Dykema, Free Products of Hyperfinite von Neumann Algebras and Free Dimension, Duke Math. J. 69 (1993), 97-119. | MR | Zbl

[Ef1] E. G. Effros, Property $Γ$ and Inner Amenability, Proc. Amer. Math. Soc. 47 (1975), 483-486. | MR | Zbl

[Ef2] E. G. Effros, Why the Circle is Connected : An Introduction to Quantized Topology, Math. Intell. 11-1 (1989), 27-34. | DOI | MR | Zbl

[ElR] G. A. Elliott and M. Rordam, The Automorphism Group of the Irrational Rotation $C^{*}$ -algebra, Preprint, Odense Univ. (1992). | MR | Zbl

[ExL] R. Exel and T. A. Loring, Finite-dimensional Representations of Free Product $C^{*}$ -algebras, International J. Math. 3 (1992), 469-476. | DOI | MR | Zbl

[FaH] T. Fack and P. De La Harpe, Sommes de commutateurs dans les algèbres de von Neumann finies continues, Ann. Inst Fourier 30-3 (1980), 49-83. | DOI | EuDML | Numdam | MR | Zbl

[Far] D. R. Farkas, Group Rings : an Annotated Questionnaire, Comm. in Algebra 8 (1980), 585-602. | DOI | MR | Zbl

[FTP] A. Figà-Talamanca and M. A. Picardello, Harmonic Analysis and Representation Theory for Groups Acting on Homogeneous Trees, Cambridge Univ. Press, 1991. | DOI | MR | Zbl

[FTN] A. Figà-Talamanca and C. Nebbia, Harmonic Analysis on Free Groups, Dekker, 1983. | MR | Zbl

[Fo1] E. Formanek, Idempotents in Noetherian Group Rings, Canadian J. Math. 25 (1973), 366-369. | DOI | MR | Zbl

[Fo2] E. Formanek, The Type I Part of the Regular Representation, Can. J. Math. 26 (1974), 1086-1089. | DOI | MR | Zbl

[For] B. Forrest, Amenability and Ideals in $A (G)$ , J. Austral. Math. Soc. (Series A) 53 (1992), 143-155. | DOI | MR | Zbl

[GhH] E. Ghys and P. De La Harpe (editors), Sur les groupes hyperboliques d'après Mikhael Gromov, Birkhäuser, 1990. | MR | Zbl

[GiH] T. Giordano and P. De La Harpe, Groupes de tresses et moyennabilité intérieure, Arkiv for Mat. 29 (1991), 63-72. | DOI | MR | Zbl

[Gla] A. M. W. Glass, The Ubiquity of Free Groups, Math. Intelligencer 14 (1992), 54-56. | DOI | MR | Zbl

[GHJ] F. Goodman, P. De La Harpe and V. Jones, Coxeter Graphs and Towers of Algebras, Springer, 1989. | DOI | MR | Zbl

[Gr1] M. Gromov, Hyperbolic Groups, in "Essays in Group Theory", edited by S.M. Gersten, Springer (1987), 75-263. | DOI | MR | Zbl

[Gr2] M. Gromov, Asymptotic Invariants of Infinite Groups, in "Geometric Group Theory, volume II", edited by G.A. Niblo and M.A. Roller, Cambridge Univ. Press (1993), 1-295. | MR | Zbl

[Haa1] U. Haagerup, An Example of a Nonnuclear $C^{*}$ -algebra which has the Metric Approximation Property, Inventiones Math. 50 (1979), 279-293. | DOI | EuDML | MR | Zbl

[Haa2] U. Haagerup, The Reduced $C^{*}$ -algebra of the Free Group on Two Generators, 18th Scandinavian Congress of Mathematicians (August 18-22, 1980). | Zbl

[Haa3] U. Haagerup, Group $C^{*}$ -algebras Without the Completely Bounded Approximation Property, Manuscript (May 1986).

[Har1] P. De La Harpe, Free Groups in Linear Groups, L'Enseignement math. 29 (1983), 129-144. | MR | Zbl

[Har2] P. De La Harpe, Reduced $C^{*}$ -algebras of Discrete Groups Which are Simple with Unique Trace, Springer Lecture Notes in Math. 1132 (1985), 230-253. | MR | Zbl

[Har3] P. De La Harpe, Groupes de Coxeter infinis non affines, Expo. Math. 5 (1987), 91-96. | MR | Zbl

[Har4] P. De La Harpe, Groupes hyperboliques, algèbres d'opérateurs et un théorème de Jolissaint, CR. Acad. Sc. Paris 307, Série I (1988), 771-774. | MR | Zbl

[Har5] P. De La Harpe, An Invitation to Coxeter Groups, in "Group Theory from a Geometric Viewpoint (26 March - 6 April 1990, Trieste), edited by E. Ghys et al., World Scientific (1991), 193-253. | MR | Zbl

[HaJ] P. De La Harpe and K. Jhabvala, Quelques propriétés des algèbres d'un groupe discontinu d'isométries hyperboliques, in "Ergodic Theory (Séminaire, Les Plans-sur-Bex, 1980)", Monographie de l'Enseignement Math. 29 (1981), 47-55. | MR | Zbl

[HRV1] P. De La Harpe, G. Robertson and A. Valette, On the Spectrum of the Sum of Generators for a Finitely Generated Group, Israel J. Math. 81 (1993), 65-96. | DOI | EuDML | MR | Zbl

[HRV2] P. De La Harpe, G. Robertson and A. Valette, On Exactness of Group $C^{*}$ -algebras, submitted to Quart. J. Math. | MR | Zbl

[HRV3] P. De La Harpe, G. Robertson and A. Valette, On the Spectrum of the Sum of Generators for a Finitely Generated Group, part II, Colloquium Math. 65 (1993), 87-102. | EuDML | MR | Zbl

[HS1] P. De La Harpe and G. Skandalis, Sur la simplicité essentielle du groupe des inversibles et du groupe unitaire dans une $C^{*}$ -algèbre simple, J. Functional Analysis 62 (1985), 354-378. | DOI | MR | Zbl

[HS2] P. De La Harpe and G. Skandalis, Powers' Property and Simple $C^{*}$ -algebras, Math. Ann. 273 (1986), 241-250. | DOI | EuDML | MR | Zbl

[HS3] P. De La Harpe and G. Skandalis, Les réseaux dans les groupes semi-simples ne sont pas intérieurement moyennables, L'Enseignement Math. (to appear). | MR | Zbl

[HaVa] P. De La Harpe and A. Valette, La propriété $(T)$ de Kazhdan pour les groupes localement compacts, Astérisque 175, Soc. Math. France, 1989. | Numdam | MR | Zbl

[HaVo] P. De La Harpe and D. Voiculescu, A Problem on the $I I_{1}$ -factors of Fuchsian Groups, These Proceedings.

[Hau] J-C. Hausmann, Sur l'usage de critères pour reconnaître un groupe libre, un produit amalgamé ou une $H N N$ -extension, l'Enseignement math. 27 (1981), 221-242. | MR | Zbl

[Hig] G. Higman, The Units of Group-rings, Proc. London Math. Soc. 46 (1940), 231-248. | DOI | JFM | MR

[HoR] R. E. Howe et J. Rosenberg, The Unitary Representation Theory of $G L (n)$ of an Infinite Discrete Field, Israel J. Math. 67 (1989), 67-81. | DOI | MR | Zbl

[Ji1] R. Ji, Smooth Dense Subalgebras of Reduced Group $C^{*}$ -algebras, Schwartz Cohomology of Groups, and Cyclic Cohomology, J. Functional Analysis, to appear. | MR | Zbl

[Ji2] R. Ji, Nilpotency of Connes' Periodic Operator and the Idempotent Conjectures, Preprint, Indiana University - Purdue University (1990). | MR | Zbl

[JiP] R. Ji and S. Pedersen, Certain Full Group $C^{*}$ -algebras without Proper Projections, J. Operator Theory 24 (1990), 239-252. | MR | Zbl

[Jo1] P. Jolissaint, Rapidly Decreasing Functions in Reduced $C^{*}$ -algebras of Groups., Trans Amer. Math. Soc. 317 (1990), 167-196. | MR | Zbl

[Jo2] P. Jolissaint, $K$ -theory of Reduced $C^{*}$ -algebras and Rapidly Decreasing Functions on Groups, K-Theory 2 (1989), 723-735. | DOI | MR | Zbl

[Jo3] P. Jolissaint, Property $T$ for Discrete Groups in Terms of their Regular Representation, Math. Annalen, to appear. | EuDML | MR | Zbl

[JoV] P. Jolissaint and A. Valette, Normes de Sobolev et convoluteurs bornés sur $L^{2} (G)$ , Ann. Inst Fourier 41-4 (1991), 797-822. | DOI | EuDML | Numdam | MR | Zbl

[Jo79] V. F. R. Jones, Notes on Connes' Invariant $_{(} M)$ , Unpublished Notes of Lectures given at Lausanne (1978/79) and elsewhere.

[Jo80] V. F. R. Jones, A $I I_{1}$ -factor Anti-isomorphic to Itself but Without Involutory Antiautomorphism, Math. Scand. 46 (1980), 103-117. | DOI | EuDML | MR | Zbl

[Jo83] V. F. R. Jones, Index for Subfactors, Inventiones Math. 72 (1983), 1-25. | DOI | EuDML | MR | Zbl

[JuK] P. Julg and G. G. Kasparov, L'anneau $K K_{G} (ℂ, ℂ)$ pour $S U (n, 1)$ , CR. Acad. Sc. Paris 313, Série I (1991), 259-264. | MR | Zbl

[KaV] V. A. Kaimanovich and A. M. Vershik, Random Walks on Discrete Groups : Boundary and Entropy, Ann. of Probability 11 (1983), 457-490. | DOI | MR | Zbl

[Ka1] R. R. Kallman, A Generalization of Free Action, Duke Math. J. 36 (1969), 781-789. | DOI | MR | Zbl

[Ka2] R. R. Kallman, A Theorem on Discrete Groups and some Consequences of Kazdan Thesis, J. Functional Analysis 6 (1970), 203-207. | DOI | MR | Zbl

[Kan] E. Kaniuth, Der Typ der regulären Darstellung diskreter Gruppen, Math. Ann. 182 (1969), 334-339. | DOI | EuDML | MR | Zbl

[KaT] E. Kaniuth and K. F. Taylor, Projections in $C^{*}$ -algebras of nilpotent groups, Manuscripta Math. 65 (1989), 93-111. | DOI | EuDML | MR | Zbl

[Kap] I. Kaplansky, Group Algebras in the Large, Tôhoku Math. J. 3 (1951), 249-256. | DOI | MR | Zbl

[Kas] G. G. Kasparov, Lorentz Groups : $K$ -theory of Unitary Representations and Crossed Products, Soviet Math. Dokl. 29 (1984), 256-260. | MR | Zbl

[Kaw] Y. Kawahigashi, Centrally Trivial Automorphisms and an Analogue of Connes' $_{χ} (M)$ for Subfactors, Duke Math. J. 71 (1993), 93-118. | DOI | MR | Zbl

[KeW] O. Kegel and B. Wehrfritz, Locally Finite Groups, North Holland, 1973. | MR | Zbl

[Ke1] H. Kesten, Symmetric Random Walks on Groups, Trans. Amer. Math. Soc. 22 (1959), 336-354. | DOI | MR | Zbl

[Ke2] H. Kesten, Full Banach Mean Values on Countable Groups, Math. Scand. 7 (1959), 146-156. | DOI | EuDML | MR | Zbl

[Ki1] E. Kirchberg, Positive Maps and $C^{*}$ -nuclear Algebras, Proceedings of the Intern. Conf. on Operator Algebras, Ideals and their Applications in Theoretical Physics (Leipzig 1977), Teubner, Leipzig (1978), 327-328. | Zbl

[Ki2] E. Kirchberg, The Fubini Theorem for Exact $C^{*}$ -algebras, J. Operator Theory 10 (1983), 3-8. | MR | Zbl

[Ki3] E. Kirchberg, On Non-semisplit Extensions, Tensor Products and Exactness of Group $C^{*}$ -algebras, Inventiones Math. 112 (1993), 449-489. | DOI | EuDML | MR | Zbl

[KiV] E. Kirchberg and G. Vaillant, On $C^{*}$ -algebras Having Linear, Polynomial and Subexponential Growth, Inventiones Math. 108 (1992), 635-652. | DOI | EuDML | MR | Zbl

[Kou] E. Kirchberg and G. Vaillant, The Kourovka Notebook (Unsolved Problems in Group Theory), Amer. Math. Soc., Translations 121, 1983

E. Kirchberg and G. Vaillant The Kourovka Notebook (Unsolved Problems in Group Theory), (see also Russian Math. Surveys 46 : 5 (1991) 137-182). | DOI

[Kle] F. Klein, Neue Beiträge zur Riemann'schen Functionentheorie, Math. Annalen 21 (1883), 141-218. | DOI | EuDML | JFM | MR

[Kum] A. Kumjian, An Involutive Automorphism of the Bunce-Deddens Algebra, C.R. Math. Rep. Acad. Sci. Canada 10 (1988), 217-218. | MR | Zbl

[La1] C. Lance, On Nuclear $C^{*}$ -algebras, J. Functional Analysis 12 (1973), 157-176. | DOI | MR | Zbl

[La2] C. Lance, Tensor Products and Nuclear $C^{*}$ -algebras, Proc. Symp. Pure Math. 38, Part I (1982), 379-399. | DOI | MR | Zbl

[LHa] M. Lemvig Hansen, Weak Amenability of the Universal Covering Group of $S U (1, n)$ , Preprint. | MR | Zbl

[Lep] H. Leptin, The Structure of $L^{1} (G)$ for locally compact groups, in "Operator Algebras and Group Representations, vol. II (Proc. Intern. Conf. Neptune, 1980)", edited by Gr. Arsene et al., Pitman (1984), 48-61. | MR | Zbl

[LuZ] A. Lubotzky and R. J. Zimmer, Variants of Kazhdan's Property for Subgroups of Semisimple Groups, Israel J. Math. 66 (1989), 289-299. | DOI | MR | Zbl

[Mac] A.M. Macbeath, Packings, Free Products and Residually Finite Groups, Proc. Camb. Phil. Soc. 59 (1963), 555-558. | DOI | MR | Zbl

[Mal] A. I. Mal'Cev, On the faithful Representations of Infinite Groups by Matrices, Amer. Math. Soc. Translations 45 (1965), 1-18. | Zbl

[Mar] O. Maréchal, Une remarque sur un théorème de Glimm, Bull. Sc. math. 99 (1975), 41-44. | MR | Zbl

[Mas] G. A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Springer, 1991. | DOI | MR | Zbl

[McD] D. Mcduff, Uncountably many $I I_{1}$ Factors, Ann. of Math. 90 (1969), 372-377. | DOI | MR | Zbl

[MNI] F. J. Murray and J. Von Neumann, On Rings of Operators, Ann. of Math. 37 (1936), 116-229 (= [vNe], 6-119). | DOI | JFM | MR | Zbl

[MNIV] F. J. Murray and J. Von Neumann, On Rings of Operators, IV, Ann. of Math. 44 (1943), 716-808 (= [vNe], 229-321). | DOI | MR | Zbl

[MyW] J. Mycielski and S. Wagon, Large Free Groups of Isometries and their Geometrical Uses, L'Enseignement Math. 30 (1984), 247-267. | MR | Zbl

[Naz] M. L. Nazarov, Projective Representations of the Infinite Symmetric Group, in "Representation Theory and Dynamical Systems", edited by A.M. Vershik, Adv. in Soviet Math. 9 (1992), 115-130. | DOI | MR | Zbl

[vNe] J. Von Neumann, Collected Works, Volume III, edited by A.H. Taub, Academic Press, 1961. | MR | Zbl

[Ogl] C. Ogle, Assembly Maps, $K$ -Theory, and Hyperbolic Groups, $K$ -Theory 6 (1992), 235-265. | DOI | MR | Zbl

[Pac] J. A. Packer, Twisted Group $C^{*}$ -algebras Corresponding to Nilpotent Discrete Groups, Math. Scand. 64 (1989), 109-122. | DOI | EuDML | MR | Zbl

[PaS] W. Paschke and N. Salinas, $C^{*}$ -algebras Associated with the Free Products of Groups, Pacific J. Math. 82 (1979), 211-221. | DOI | MR | Zbl

[Pat] A. T. Paterson, Amenability, Math. Surveys and Monographs 29, Amer. Math. Soc., 1988. | DOI | MR | Zbl

[Ped] G. K. Pedersen, $C^{*}$ -algebras and their Automorphism Groups, Academic Press, 1979. | MR | Zbl

[Phi] J. Phillips, Outer Automorphisms of Separable $C^{*}$ -algebras., J. Functional Analysis 70 (1987), 111-116. | DOI | MR | Zbl

[Pim] M. Pimsner, $K K$ -groups of Crossed Products by Groups Acting on Trees, Inventiones Math. 86 (1986), 603-634. | DOI | EuDML | MR | Zbl

[PiP] M. Pimsner and S. Popa, Sur les sous-facteurs d'indice fini d'un facteur de type $I I_{1}$ ayant la propriété $T$ ., C.R. Acad. Sc. Paris 303, Série I (1986), 359-361. | MR | Zbl

[PiV] M. Pimsner and D. Voiculescu, $K$ -groups of Reduced Crossed Products by Free Groups, J. Operator Theory 8 (1982), 131-156. | MR | Zbl

[Po1] S. Popa, Orthogonal Pairs of $^{*}$ -algebras in Finite von Neumann Algebras, J. Operator Theory 9 (1983), 253-268. | MR | Zbl

[Po2] S. Popa, Maximal Injective Subalgebras in Factors Associated with Free Groups, Advances in Math. 50 (1983), 27-48. | DOI | MR | Zbl

[Po3] S. Popa, Notes on Cartan Subalgebras in Type $I I_{1}$ Factors, Math. Scand. 57 (1985), 171-188. | DOI | EuDML | MR | Zbl

[Po4] S. Popa, Correspondences, Preprint (1986).

[Po5] S. Popa, Some Rigidity Results in Type $I I_{1}$ Factors, C.R. Acad. Sc. Paris 311, Série I (1990), 535-538. | MR | Zbl

[Po6] S. Popa, Free-independent Sequences in Type $I I_{1}$ Factors and Related Problems, Preprint, UCLA (1992).

[PoT] S. Popa and M. Takesaki, The Topological Structure of the Unitary and Automorphism Groups of a Factor, Preprint, UCLA (1992). | Zbl

[Pow] R. T. Powers, Simplicity of the $C^{*}$ -algebra Associated with the Free Group on Two Generators, Duke Math. J. 42 (1975), 151-156. | DOI | MR | Zbl

[Pro] S. D. Promislov, A Class of Groups Producing Simple, Unique Trace, $C^{*}$ -algebras, Math. Proc. Camb. Phil. Soc. 114 (1993), 223-233. | DOI | MR | Zbl

[Ra1] F. Radulescu, The Fundamental Group of the von Neumann Algebra of a Free Group with Infinitely Many Generators is $ℝ_{+} - 0$ , J. of Amer. Math. Soc. 5 (1992), 517-532. | MR | Zbl

[Ra2] F. Radulescu, A One Parameter Group of Automorphisms of $ℒ (F \infty) \otimes B (H)$ scaling the trace, C.R. Acad. Sci. Paris 314, Série I (1992), 1027-1032. | MR | Zbl

[Ra3] F. Radulescu, Sous-facteurs de $ℒ (F \infty)$ d'indice $4 {cos}^{2} \frac{π}{n}, n \geq 3$ , C.R. Acad. Sci. Paris 315, Série I (1992), 37-42. | MR | Zbl

[Ra4] F. Radulescu, Stable Equivalence of the Weak Closures of Free Groups Convolution Algebras, Preprint, Univ. of Berkeley (1992). | MR | Zbl

[Ra5] F. Radulescu, Random Matrices, Amalgamated Free Products and Subfactors of the von Neumann Algebra of a Free Group, of Noninteger Index, Preprint, IHES (1991) | MR | Zbl

[Rag] M. S. Raghunathan, Discrete Subgroups of Lie Groups, Springer, 1972. | DOI | MR | Zbl

[Rei] K. Reidemeister, Einführung in die kombinatorische Topologie, Vieweg, 1932. | JFM | MR | Zbl

[Rin] J. R. Ringrose, Cohomology of Operator Algebras, Lecture Notes in Math. 247 (Springer, 1972), 355-434. | MR | Zbl

[Rob] A. G. Robertson, Property $(T)$ for $I I_{1}$ Factors and Unitary Representations of Kazhdan Groups, Math. Ann. 296 (1993), 547-555. | DOI | EuDML | MR | Zbl

[Ros] J. Rosenberg, Un complément à un théorème de Kirillov sur les caractères de $G L (n)$ d'un corps infini discret, C.R. Acad. Sc. Paris 309, Série I (1989), 581-586. | MR | Zbl

[Sai] T. Saitô, Generations of von Neumann Algebras, Lecture Notes in Math. 247 (Springer, 1972), 435-531. | MR | Zbl

[Sak] S. Sakai, $C^{*}$ -algebras and $W^{*}$ -algebras, Springer, 1971. | MR | Zbl

[Sch] G. Schlichting, Eine Charakterisierung gewisser diskreter Gruppen durch ihre reguläre Darstellung, Manuscripta Math. 9 (1973), 389-409. | DOI | EuDML | MR | Zbl

[Sc1] H. Schröder, On the Homotopy Type of the Regular Group of a $W^{*}$ -algebra, Math. Ann. 267 (1984), 271-277. | DOI | EuDML | MR | Zbl

[Sc2] H. Schröder, On the Topology of the Group Invertible Elements - A Survey, Preprint, Dortmund (1992).

[Seg] I. E. Segal, Irreducible Representations of Operator Algebras, Bull. Amer. Math. Soc. 53 (1947), 73-88. | DOI | MR | Zbl

[Ser] J-P. Serre, Arbres, amalgames, $S L_{2}$ , Astérisque 46, Soc. Math. France, 1977. | Numdam | MR | Zbl

[Sk1] G. Skandalis, Une notion de nucléarité en $K$ -théorie (d'après J. Cuntz), $K$ -Theory 1 (1988), 549-573. | DOI | MR | Zbl

[Sk2] G. Skandalis, Algèbres de von Neumann de groupes libres et probabilités non commutatives (d'après Voiculescu et al), Séminaire Bourbaki 764 (novembre 1992). | EuDML | Numdam | MR | Zbl

[Sm1] M. Smith, Regular Representations of Discrete Groups, J. Functional Analysis 11 (1972), 401-406. | DOI | MR | Zbl

[Sm2] M. Smith, Regular Representations of Unimodular Groups, Math. Ann. 203 (1973), 183-185. | DOI | EuDML | MR | Zbl

[Sto] E. Stormer, Entropy of Some Automorphisms of the II1-factor of the Free Group in Infinite Number of Generators, Inventiones Math. 110 (1992), 63-73. | DOI | EuDML | MR | Zbl

[Sun] T. Sunada, Group $C^{*}$ -algebras and the Spectrum of a Periodic Schrödinger Operator on a Manifold, Can. J. Math. 44 (1992), 180-193. | DOI | MR | Zbl

[Swa] R. G. Swan, Group of Cohomological Dimension One, J. of Algebra 12 (1969), 585-601. | DOI | MR | Zbl

[Sz1] R. Szwarc, An Analytic Series of Irreducible Representations of the Free Group, Ann. Inst. Fourier 38-1 (1988), 87-110. | DOI | EuDML | Numdam | MR | Zbl

[Sz2] R. Szwarc, A Short Proof of the Grigorchuk-Cohen Cogrowth Theorem, Proc. Amer. Math. Soc. 106 (1989), 663-665. | DOI | MR | Zbl

[Sz3] R. Szwarc, Group Acting on Trees and Approximation Properties of the Fourier Algebra, J. Functional Analysis 95 (1991), 320-343. | DOI | MR | Zbl

[Ta1] M. Takesaki, On the Cross-norm of the Direct Product of $C^{*}$ -algebras, Tôhoku Math. J. 16 (1964), 11-122. | DOI | MR | Zbl

[Ta2] M. Takesaki, Theory of Operator Algebras I, Springer, 1979. | DOI | MR | Zbl

[Tho] E. Thoma, Ein Charakterisierung diskreter Gruppen vom Typ I, Inventiones Math. 6 (1968), 190-196. | DOI | EuDML | MR | Zbl

[Tit] J. Tits, Free Subgroups in Linear Groups, J. of Algebra 20 (1972), 250-270. | DOI | MR | Zbl

[Tom] M. J. Tomkinson, $F C$ -groups, Pitman, 1984. | MR | Zbl

[Va1] A. Valette, Minimal Projections, Integrable Representations and Property $(T)$ , Arch. Math. 43 (1984), 397-406. | DOI | MR | Zbl

[Va2] A. Valette, The Conjecture of Idempotents : a Survey of the $C^{*}$ -algebraic Approach, Bull. Soc. Math. Belg. 46 (1989), 485-521. | MR | Zbl

[Va3] A. Valette, Les représentations uniformément bornées associées à un arbre réel, Bull. Soc. Math. Belgique, Série A 42 (1990), 747-760. | MR | Zbl

[Va4] A. Valette, Weak Amenability of Right Angled Coxeter Group, Proc. Amer. Math. Soc. (to appear). | MR | Zbl

[Va5] A. Valette, Projections in Full $C^{*}$ -algebras of Semisimple Groups, Math. Ann. 294 (1992), 277-287. | DOI | EuDML | MR | Zbl

[Vo1] D. Voiculescu, A Non-commutative Weyl-von Neumann Theorem, Rev. Roumaine Math. Pures Appl. 21 (1976), 97-113. | MR | Zbl

[Vo2] D. Voiculescu, Circular and Semicircular Systems and Free Product Factors, in "Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory (Actes du colloque en l'honneur de Jacques Dixmier)", edited by A. Connes et al., Birkhäuser (1990), 45-60. | MR | Zbl

[VDN] D. Voiculescu, K. J. Dykema and A. Nica, Free Random Variables, CRM Monograph Series, Amer. Math. Soc., 1992. | DOI | MR | Zbl

[Wa1] M. E. Walter, $W^{*}$ -algebras and Nonabelian Harmonic Analysis, J. Functional Analysis 11 (1972), 17-38. | DOI | MR | Zbl

[Wa2] M. E. Walter, A Duality Between Locally Compact Groups and Certain Banach Algebras, J. Functional Analysis 17 (1974), 131-160. | DOI | MR | Zbl

[Wag] S. Wagon, The Banach-Tarski Paradox, Cambridge Univ. Press, 1985. | DOI | MR | Zbl

[Was1] S. Wassermann, On Tensor Products of Certain Group $C^{*}$ -algebras, J. Functional Analysis 23 (1976), 239-254. | DOI | MR | Zbl

[Was2] S. Wassermann, Tensor Products of Free-Group $C^{*}$ -algebras, Bull. London Math. Soc. 22 (1990), 375-380. | DOI | MR | Zbl

[Wat] Y. Watatani, The Character Groups of Amenable Group $C^{*}$ -algebras, Math. Japonica 24 (1979), 141-144. | MR | Zbl

[Wen] J. G. Wendel, Left Centralizers and Isomorphisms of Group Algebras, Pacific J. Math. 2 (1952), 251-261. | DOI | MR | Zbl

[Woe] W. Woess, Cogrowth of Groups and Simple Random Walks, Arch. Math. 41 (1983), 363-370. | DOI | MR | Zbl

[Yos] H. Yoshizawa, Some Remarks on Unitary Representations of the Free Group, Osaka Math. J. 3 (1951), 55-63. | MR | Zbl

[Zim] R. J. Zimmer, Ergodic Theory and Semisimple Groups, Birkhäuser, 1984. | MR | Zbl