Lie theory and the Chern-Weil homomorphism
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 38 (2005) no. 2, pp. 303-338.
DOI: 10.1016/j.ansens.2004.11.004
Alekseev, Anton 1; Meinrenken, Eckhard 2

1 Université de Genève, Section de Mathématiques, 2-4 rue du Lièvre, Case Postale 240, 1211 Genève 24 (Suisse)
2 University of Toronto, Department of Mathematics, 100 St George Street, Toronto, Ont. (Canada)
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Alekseev, Anton; Meinrenken, Eckhard. Lie theory and the Chern-Weil homomorphism. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 38 (2005) no. 2, pp. 303-338. doi : 10.1016/j.ansens.2004.11.004. http://archive.numdam.org/articles/10.1016/j.ansens.2004.11.004/

[1] Alekseev A., Meinrenken E., The non-commutative Weil algebra, Invent. Math. 139 (2000) 135-172. | MR | Zbl

[2] Alekseev A., Meinrenken E., Poisson geometry and the Kashiwara-Vergne conjecture, C. R. Math. Acad. Sci. Paris 335 (9) (2002) 723-728. | MR | Zbl

[3] Alekseev A., Meinrenken E., Clifford algebras and the classical dynamical Yang-Baxter equation, Math. Res. Lett. 10 (2-3) (2003) 253-268. | MR | Zbl

[4] Alekseev A., Meinrenken E., Woodward C., Linearization of Poisson actions and singular values of matrix products, Ann. Inst. Fourier (Grenoble) 51 (6) (2001) 1691-1717. | Numdam | MR | Zbl

[5] Andler M., Dvorsky A., Sahi S., Deformation quantization and invariant distributions, C. R. Acad. Sci. Paris Sér. I Math. 330 (2) (2000) 115-120, math.QA/9905065. | MR | Zbl

[6] Andler M., Dvorsky A., Sahi S., Kontsevich quantization and invariant distributions on Lie groups, Ann. Sci. École Norm. Sup. (4) 35 (3) (2002) 371-390. | Numdam | MR | Zbl

[7] Andler M., Sahi S., Torossian C., Convolution of invariant distributions: Proof of the Kashiwara-Vergne conjecture, Lett. Math. Phys. 69 (2004) 177-203. | MR | Zbl

[8] Bott R., Lectures on characteristic classes and foliations, in: Lectures on Algebraic and Differential Topology (Second Latin American School in Math., Mexico City, 1971), Lecture Notes in Math., vol. 279, Springer, Berlin, 1972, pp. 1-94, Notes by Lawrence Conlon, with two appendices by J. Stasheff. | MR | Zbl

[9] Cartan H., Notions d'algèbre différentielle; application aux groupes de Lie et aux variétés où opère un groupe de Lie, in: Colloque de topologie (espaces fibrés) (Bruxelles) Georges Thone, Liège, Masson et Cie, Paris, 1950. | Zbl

[10] Chern S.S., Characteristic classes of Hermitian manifolds, Ann. of Math. (2) 47 (1946) 85-121. | MR | Zbl

[11] Corwin L., Ne'Eman Y., Sternberg S., Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry), Rev. Modern Phys. 47 (1975) 573-603. | MR | Zbl

[12] Deligne P., Morgan J., Notes on supersymmetry (following Joseph Bernstein), in: Quantum Fields and Strings: A Course for Mathematicians, vols. 1, 2 (Princeton, NJ, 1996/1997), Amer. Math. Soc., Providence, RI, 1999, pp. 41-97. | MR | Zbl

[13] Duflo M., Opérateurs différentiels bi-invariants sur un groupe de Lie, Ann. Sci. École Norm. Sup. 10 (1977) 265-288. | Numdam | MR | Zbl

[14] Duflo M., Opérateurs différentiels invariants sur un espace symétrique, C. R. Acad. Sci. Paris Sér. 289 (2) (1979) A135-A137. | MR | Zbl

[15] Duistermaat J.J., On the similarity between the Iwasawa projection and the diagonal part, Mém. Soc. Math. France (NS) 15 (1984) 129-138, Harmonic analysis on Lie groups and symmetric spaces (Kleebach, 1983). | Numdam | MR | Zbl

[16] Dupont J.L., Simplicial de Rham cohomology and characteristic classes of flat bundles, Topology 15 (3) (1976) 233-245. | MR | Zbl

[17] Gelfand I.M., Smirnov M.M., The algebra of Chern-Simons classes, the Poisson bracket on it, and the action of the gauge group, in: Lie Theory and Geometry, Progr. Math., vol. 123, Birkhäuser Boston, Boston, MA, 1994, pp. 261-288. | MR | Zbl

[18] Guillemin V., Sternberg S., Supersymmetry and Equivariant de Rham Theory, Springer-Verlag, Berlin, 1999. | MR | Zbl

[19] Helgason S., Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978. | MR | Zbl

[20] Huang J.-H., Pandzic P., Dirac cohomology, unitary representations and a proof of a conjecture of Vogan, J. Amer. Math. Soc. 15 (1) (2002) 185-202, (electronic). | MR | Zbl

[21] Kac V., Vertex Algebras for Beginners, University Lecture Series, vol. 10, Amer. Math. Soc., Providence, RI, 1998. | MR | Zbl

[22] Kalkman J., A BRST model applied to symplectic geometry, Ph.D. thesis, Universiteit Utrecht, 1993.

[23] Kashiwara M., Vergne M., The Campbell-Hausdorff formula and invariant hyperfunctions, Invent. Math. 47 (1978) 249-272. | MR | Zbl

[24] Knapp A.W., Lie Groups Beyond an Introduction, Progr. Math., vol. 140, Birkhäuser Boston, Boston, MA, 2002, MR 2003c:22001. | MR | Zbl

[25] Kostant B., A cubic Dirac operator and the emergence of Euler number multiplets of representations for equal rank subgroups, Duke Math. J. 100 (3) (1999) 447-501. | MR | Zbl

[26] Kostant B., Sternberg S., Symplectic reduction, BRS cohomology, and infinite-dimensional Clifford algebras, Ann. Phys. 176 (1987) 49-113. | MR | Zbl

[27] Kostant B., Dirac cohomology for the cubic Dirac operator, in: Studies in memory of Issai Schur (Chevaleret/Rehovot, 2000), Progr. Math., vol. 210, Birkhäuser Boston, Boston, MA, 2003, pp. 69-93. | MR | Zbl

[28] Kumar S., A remark on universal connections, Math. Ann. 260 (4) (1982) 453-462, MR 84d:53028. | MR | Zbl

[29] Kumar S., Induction functor in non-commutative equivariant cohomology and Dirac cohomology. | Zbl

[30] Lichnerowicz A., Opérateurs différentiels invariants sur un espace symétrique, C. R. Acad. Sci. Paris 256 (1963) 3548-3550. | MR | Zbl

[31] Lichnerowicz A., Opérateurs différentiels invariants sur un espace homogène, Ann. Sci. École Norm. Sup. (3) 81 (1964) 341-385. | Numdam | MR | Zbl

[32] Markl M., Homotopy algebras are homotopy algebras, Forum. Math. 16 (1) (2004) 129-160. | MR | Zbl

[33] May J.P., Simplicial Objects in Algebraic Topology, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1992, Reprint of the 1967 original. | MR | Zbl

[34] Medina A., Revoy Ph., Caractérisation des groupes de Lie ayant une pseudo-métrique bi-invariante. Applications, in: South Rhone Seminar on Geometry, III (Lyon, 1983), Travaux en Cours, Hermann, Paris, 1984, pp. 149-166. | MR | Zbl

[35] Mostow M., Perchik J., Notes on Gelfand-Fuks cohomology and characteristic classes (lectures delivered by R. Bott), in: Proceedings of the Eleventh Annual Holiday Symposium, New Mexico State University, 1973, pp. 1-126.

[36] Narasimhan M.S., Ramanan S., Existence of universal connections, Amer. J. Math. 83 (1961) 563-572. | MR | Zbl

[37] Rouvière F., Espaces symétriques et méthode de Kashiwara-Vergne, Ann. Sci. École Norm. Sup. (4) 19 (4) (1986) 553-581. | Numdam | MR | Zbl

[38] Segal G., Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math. 34 (1968) 105-112. | Numdam | MR | Zbl

[39] Severa P., Some titles containing the words “homotopy” and “symplectic”, e.g. this one, math.SG/0105080.

[40] Shulman H., On characteristic classes, 1972, Ph.D. thesis, Berkeley.

[41] Torossian C., Méthodes de Kashiwara-Vergne-Rouvière pour les espaces symétriques, in: Noncommutative Harmonic Analysis, Progr. Math., vol. 220, Birkhäuser Boston, Boston, MA, 2004, pp. 459-486. | MR | Zbl

[42] Torossian C., Paires symétriques orthogonales et isomorphisme de Rouvière, J. Lie Theory 15 (1) (2005) 79-87. | MR | Zbl

[43] Vergne M., Le centre de l'algèbre enveloppante et la formule de Campbell-Hausdorff, C. R. Acad. Sci. Paris Sér. I Math. 329 (9) (1999) 767-772. | MR | Zbl

[44] Weil A., Géométrie différentielle des espaces fibrés (Letters to Chevalley and Koszul), 1949, in: Oeuvres scientifiques, vol. 1, Springer, Berlin, 1979.

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