Formes différentielles invariantes à gauche sur le groupe quantique GL p,q (2)
Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Conférences de A. Aspect, B. Carter, R. Coquereaux, G.W. Gibbons, Ch. Kassel, Y. Kosman-Schwarzbach, S. Majid, G. Maltsiniotis, P. Pansu, G.A. Vilkovisky, Z. Wojtkowiak, Tome 43 (1992), Exposé no. 9, 18 p.
@article{RCP25_1992__43__163_0,
     author = {Maltsiniotis, G.},
     title = {Formes diff\'erentielles invariantes \`a gauche sur le groupe quantique $GL_{p,q}(2)$},
     journal = {Les rencontres physiciens-math\'ematiciens de Strasbourg -RCP25},
     note = {talk:9},
     pages = {163--180},
     publisher = {Institut de Recherche Math\'ematique Avanc\'ee - Universit\'e Louis Pasteur},
     volume = {43},
     year = {1992},
     language = {fr},
     url = {http://archive.numdam.org/item/RCP25_1992__43__163_0/}
}
TY  - JOUR
AU  - Maltsiniotis, G.
TI  - Formes différentielles invariantes à gauche sur le groupe quantique $GL_{p,q}(2)$
JO  - Les rencontres physiciens-mathématiciens de Strasbourg -RCP25
N1  - talk:9
PY  - 1992
SP  - 163
EP  - 180
VL  - 43
PB  - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
UR  - http://archive.numdam.org/item/RCP25_1992__43__163_0/
LA  - fr
ID  - RCP25_1992__43__163_0
ER  - 
%0 Journal Article
%A Maltsiniotis, G.
%T Formes différentielles invariantes à gauche sur le groupe quantique $GL_{p,q}(2)$
%J Les rencontres physiciens-mathématiciens de Strasbourg -RCP25
%Z talk:9
%D 1992
%P 163-180
%V 43
%I Institut de Recherche Mathématique Avancée - Université Louis Pasteur
%U http://archive.numdam.org/item/RCP25_1992__43__163_0/
%G fr
%F RCP25_1992__43__163_0
Maltsiniotis, G. Formes différentielles invariantes à gauche sur le groupe quantique $GL_{p,q}(2)$. Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Conférences de A. Aspect, B. Carter, R. Coquereaux, G.W. Gibbons, Ch. Kassel, Y. Kosman-Schwarzbach, S. Majid, G. Maltsiniotis, P. Pansu, G.A. Vilkovisky, Z. Wojtkowiak, Tome 43 (1992), Exposé no. 9, 18 p. http://archive.numdam.org/item/RCP25_1992__43__163_0/

[Ab] E. Abe, "Hopf algebras," Cambridge Tracts in Math. 74, Cambridge Univ. Press, 1980. | MR | Zbl

[Ao1] K. Aomoto, q-analogue of the de Rham cohomology associated with Jackson integrals. I, Proc. Japan Acad. 66 (A) (1990), 161-164. | MR | Zbl

[Ao2] K. Aomoto, q-analogue of the de Rham cohomology associated with Jackson integrals. II, Proc. Japan Acad. 66 (A) (1990), 240-244. | MR | Zbl

[Ao3] K. Aomoto, Finiteness of a cohomology associated with certain Jackson integrals, Tôhoku Math. J. 43 (1991), 75-101. | MR | Zbl

[AST] M. Artin, W. Schelter, J. Tate, Quantum deformations of GLn, Comm. Pure Appl. Math. 44 (1991), 879-895. | MR | Zbl

[Be] G. M. Bergman, The diamond lemma for ring theory, Adv. Math. 29 (1978), 178-218. | MR | Zbl

[Bd] D. Bernard, Quantum Lie algebras and differential calculus on quantum groups, Preprint (1990). | MR | Zbl

[Bo] N. Bourbaki, "Eléments de Mathématique," Algèbre, Chapitres 1 à 3, Hermann, Paris, 1970. | Zbl

[Br] T. Brzezinski, Exterior bialgebras, Preprint (1991).

[BDR] T. Brzezinski, H. Dabrowsky, J. Rembieliński, On the quantum differential calculus and the quantum holomorphicity, J. Math. Phys. 33, 1 (1992), 19-24. | MR | Zbl

[CSWW] U. Carow-Watamura, M. Schlieker, S. Watamura, W. Weich, Bicovariant differential calculus on quantum groups SUq(N) and SOq(N), Commun. Math. Phys. 142 (1991), 605-641. | MR | Zbl

[Ca] P. Cartier, Calcul différentiel non commutatif, Exposés à l'E.N.S. (1989).

[Co] A. Connes, Non-commutative differential geometry, Publications Mathématiques de l'I.H.E.S. 62 (1985), 41-144. | EuDML | Numdam | Zbl

[DM] P. Deligne, J. S. Milne, Tannakian categories, in "Hodge cycles, motives, and Shimura varieties," Lecture Notes in Mathematics 900, Springer-Verlag, 1982, pp. 101-228. | MR | Zbl

[Dr] V. G. Drinfel'D, Quantum groups, in "Proceedings of the International Congress of Mathematicians 1986, Berkeley," AMS, 1987, pp. 798-820. | MR | Zbl

[DV1] M. Dubois-Violette, Dérivations et calcul différentiel non commutatif, C.R.A.S. 307 (1988), 403-408. | MR | Zbl

[DV2] M. Dubois-Violette, Noncommutative differential geometry, quantum mechanics and gauge theory, Preprint, L.P.T.H.E.-Orsay 90/31 (1990). | MR | Zbl

[DKM1] M. Dubois-Violette, R. Kerner, J. Madore, Noncommutative differential geometry of matrix algebras, J. Math. Phys. 31, 2 (1990), 316-322. | MR | Zbl

[DKM2] M. Dubois-Violette, R. Kerner, J. Madore, Noncommutative differential geometry and new models of gauge theory, J. Math. Phys. 31, 2 (1990), 323-330. | MR | Zbl

[FT] P. Feng, B. Tsygan, Hochschild and cyclic homology of quantum groups, Commun. Math. Phys. 140 (1991), 481-521. | MR | Zbl

[EGA IV4] A. Grothendieck, "Éléments de géométrie algébrique IV," Publications Mathématiques de l'I.H.E.S. 32, 1967. | Numdam | Zbl

[Gr] A. Grothendieck, On the De Rham cohomology of algebraic varieties, Publications Mathématiques de l'I.H.E.S. 29 (1966), 95-103. | EuDML | Numdam | MR | Zbl

[GRR] D. Gurevich, A. Radul, V. Rubtsov, Non-commutative differential geometry and Yang-Baxter equation, Preprint (1990). | Zbl

[HW] T. Hibi, M. Wakayama, A q-analogue of Capelli's identity for GL(2), Preprint, Hokkaido University (1991). | MR | Zbl

[J1] M. Jimbo, A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), 63-69. | MR | Zbl

[J2] M. Jimbo, Quantum R matrix for the generalized Toda system, Commun. Math. Phys. 102 (1986), 537-547. | MR | Zbl

[J3] M. Jimbo, A q-analogue of U(gl(N + 1)), Hecke algebras and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), 247-252. | MR | Zbl

[Ju] B. Jurčo, Differential Calculus On Quantized Simple Lie Groups, Lett. Math. Phys. 22 (1991), 177-186. | MR | Zbl

[Ka] M. Karoubi, "Homologie cyclique et K-théorie," Asterisque 149, 1987. | Numdam | MR | Zbl

[Kas] C. Kassel, Cyclic homology of differential operators, the Virasoro algebra and a q-analogue, Preprint (1991). | MR | Zbl

[Mal1] G. Maltsiniotis, Groupes quantiques et structures différentielles, C.R.A.S. 311, Sér. I (1990), 831-834. | MR | Zbl

[Mal2] G. Maltsiniotis, Calcul différentiel sur le groupe linéaire quantique, Preprint (1990).

[Mal3] G. Maltsiniotis, Groupoïdes quantiques, C.R.A.S. 314, Sér. I (1992), 249-252. | MR | Zbl

[Mal4] G. Maltsiniotis, Le langage des espaces et des groupes quantiques, Preprint (1992). | MR | Zbl

[Man1] Yu. I. Manin, Some remarks on Koszul algebras and quantum groups, Ann. Inst. Fourier 37, 4 (1987), 191-205. | EuDML | Numdam | MR | Zbl

[Man2] Yu. I. Manin, "Quantum groups and non-commutative geometry," Centre de Recherches Mathématiques de l'Université de Montréal, 1988. | MR | Zbl

[Man3] Yu. I. Manin, Multiparametric quantum deformation of the general linear supergroup, Commun. Math. Phys. 123 (1989), 163-175. | MR | Zbl

[Man4] Yu. I. Manin, Notes on quantum groups and quantum de Rham complexes, Preprint, MPI/91-60 (1991). | MR | Zbl

[MNW1] T. Masuda, Y. Nakagami, J. Watanabe, Noncommutative differential geometry on the quantum SU(2), I: An algebraic viewpoint, K-Theory 4 (1990), 157-180. | MR | Zbl

[MNW2] T. Masuda, Y. Nakagami, J. Watanabe, Noncommutative differential geometry on the quantum two sphere of Podles, I: An algebraic viewpoint, K-Theory 5 (1991), 151-175. | MR | Zbl

[M-H] F. Müller-Hoissen, Differential calculi on the quantum group GL p,q (2), Preprint, GOET-TP55/91 (1991). | Zbl

[NUW] M. Noumi, T. Umeda, M. Wakayama, A quantum analogue of the Capelli identity and an elementary differential calculus on GL q (n), Preprint, University of Tokyo (1991). | MR | Zbl

[Po] P. Podles, Differential calculus on quantum spheres, Lett. Math. Phys. 18 (1989), 107-119. | MR | Zbl

[Pr] S. B. Priddy, Koszul resolutions, Trans. Amer. Math. Soc. 152 (1970), 39-60. | MR | Zbl

[RTF] N. Yu. Reshetikhin, L. A. Takhtadzhyan, L. D. Fadeev, Quantization of Lie groups and Lie algebras, Len. Math. J. 1, 1 (1990), 193-225. | MR | Zbl

[Ro] M. Rosso, Algèbres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul différentiel non commutatif, Duke Math. J. 61, 1 (1990), 11-40. | MR | Zbl

[Sch] A. Schirrmacher, Remarks on the use of R-matrices, Preprint (1991). | MR | Zbl

[SWZ] A. Schirrmacher, J. Wess, B. Zumino, The two-parameter deformation of GL(2), its differential calculus, and Lie algebra, Z. Phys. C - Particles and Fields 49 (1991), 317-324. | MR

[SVZ] W. B. Schmidke, S. P. Vokos, B. Zumino, Differential geometry of the quantum supergroup GL q (1|1), Z. Phys. C - Particles and Fields 48 (1990), 249-255. | MR | Zbl

[Su] A. Sudbery, Consistent multiparameter quantisation of GL(n), J. Phys. A: Math. Gen. 23 (1990), L697-L704. | MR | Zbl

[Ta] L. A. Takhtadzhyan, Noncommutative homology of quantum tori, Funct. Anal, and Appl. 23, 2 (1989), 147-149. | MR | Zbl

[Tsy] B. Tsygan, Notes on differential forms on quantum groups, Preprint (1991). | MR | Zbl

[WZ] J. Wess, B. Zumino, Covariant differential calculus on the quantum hyperplane, Preprint (1990). | MR | Zbl

[Wo1] S. L. Woronowicz, Twisted SU(2) group. An example of a non-commutative differential calculus, Publ. RIMS 23 (1987), 117-181. | MR | Zbl

[Wo2] S. L. Woronowicz, Differential calculus on compact matrix pseudogroups (quantum groups), Commun. Math. Phys. 122 (1989), 125-170. | MR | Zbl

[Za1] S. Zakrzewski, A differential structure for quantum mechanics, J. of Geom. and Phys. 2, 3 (1985), 135-145. | MR | Zbl

[Za2] S. Zakrzewski, Quantum and classical pseudogroups. Part II. Differential and symplectic pseudogroups, Commun. Math. Phys. 134 (1990), 371-395. | MR | Zbl