Formes différentielles invariantes à gauche sur le groupe quantique $G{L}_{p,q}\left(2\right)$

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1. [Ab] E. Abe, "Hopf algebras," Cambridge Tracts in Math.74, Cambridge Univ. Press, 1980. Zbl0476.16008MR594432
2. [Ao1] K. Aomoto, q-analogue of the de Rham cohomology associated with Jackson integrals. I, Proc. Japan Acad.66 (A) (1990), 161-164. Zbl0718.33011MR1078398
3. [Ao2] K. Aomoto, q-analogue of the de Rham cohomology associated with Jackson integrals. II, Proc. Japan Acad.66 (A) (1990), 240-244. Zbl0718.33012MR1077605
4. [Ao3] K. Aomoto, Finiteness of a cohomology associated with certain Jackson integrals, Tôhoku Math. J.43 (1991), 75-101. Zbl0769.33016MR1088716
5. [AST] M. Artin, W. Schelter, J. Tate, Quantum deformations of GLn, Comm. Pure Appl. Math.44 (1991), 879-895. Zbl0753.17015MR1127037
6. [Be] G. M. Bergman, The diamond lemma for ring theory, Adv. Math.29 (1978), 178-218. Zbl0326.16019MR506890
7. [Bd] D. Bernard, Quantum Lie algebras and differential calculus on quantum groups, Preprint (1990). Zbl0784.17015MR1182161
8. [Bo] N. Bourbaki, "Eléments de Mathématique," Algèbre, Chapitres 1 à 3, Hermann, Paris, 1970. Zbl0211.02401
9. [Br] T. Brzezinski, Exterior bialgebras, Preprint (1991). 
10. [BDR] T. Brzezinski, H. Dabrowsky, J. Rembieliński, On the quantum differential calculus and the quantum holomorphicity, J. Math. Phys.33, 1 (1992), 19-24. Zbl0753.17017MR1141497
11. [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. Zbl0743.17015MR1138053
12. [Ca] P. Cartier, Calcul différentiel non commutatif, Exposés à l'E.N.S. (1989). 
13. [Co] A. Connes, Non-commutative differential geometry, Publications Mathématiques de l'I.H.E.S.62 (1985), 41-144. Zbl0592.46056
14. [DM] P. Deligne, J. S. Milne, Tannakian categories, in "Hodge cycles, motives, and Shimura varieties," Lecture Notes in Mathematics900, Springer-Verlag, 1982, pp. 101-228. Zbl0477.14004MR654325
15. [Dr] V. G. Drinfel'd, Quantum groups, in "Proceedings of the International Congress of Mathematicians 1986, Berkeley," AMS, 1987, pp. 798-820. Zbl0667.16003MR934283
16. [DV1] M. Dubois-Violette, Dérivations et calcul différentiel non commutatif, C.R.A.S.307 (1988), 403-408. Zbl0661.17012MR965807
17. [DV2] M. Dubois-Violette, Noncommutative differential geometry, quantum mechanics and gauge theory, Preprint, L.P.T.H.E.-Orsay90/31 (1990). Zbl0744.53042MR1134141
18. [DKM1] M. Dubois-Violette, R. Kerner, J. Madore, Noncommutative differential geometry of matrix algebras, J. Math. Phys.31, 2 (1990), 316-322. Zbl0704.53081MR1034167
19. [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. Zbl0704.53082MR1034168
20. [FT] P. Feng, B. Tsygan, Hochschild and cyclic homology of quantum groups, Commun. Math. Phys.140 (1991), 481-521. Zbl0743.17020MR1130695
21. [EGA IV4] A. Grothendieck, "Éléments de géométrie algébrique IV," Publications Mathématiques de l'I.H.E.S.32, 1967. Zbl0153.22301
22. [Gr] A. Grothendieck, On the De Rham cohomology of algebraic varieties, Publications Mathématiques de l'I.H.E.S.29 (1966), 95-103. Zbl0145.17602MR199194
23. [GRR] D. Gurevich, A. Radul, V. Rubtsov, Non-commutative differential geometry and Yang-Baxter equation, Preprint (1990). 
24. [HW] T. Hibi, M. Wakayama, A q-analogue of Capelli's identity for GL(2), Preprint, Hokkaido University (1991). Zbl0937.17009MR1351325
25. [J1] M. Jimbo, A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys.10 (1985), 63-69. Zbl0587.17004MR797001
26. [J2] M. Jimbo, Quantum R matrix for the generalized Toda system, Commun. Math. Phys.102 (1986), 537-547. Zbl0604.58013MR824090
27. [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. Zbl0602.17005MR841713
28. [Ju] B. Jurčo, Differential calculus on quantized simple Lie groups, Lett. Math. Phys.22 (1991), 177-186. Zbl0753.17020MR1129172
29. [Ka] M. Karoubi, "Homologie cyclique et K-théorie," Asterisque149, 1987. Zbl0648.18008MR913964
30. [Kas] C. Kassel, Cyclic homology of differential operators, the Virasoro algebra and a q-analogue, Preprint (1991). Zbl0761.17020MR1165187
31. [Mal1] G. Maltsiniotis, Groupes quantiques et structures différentielles, C.R.A.S.311, Sér. I (1990), 831-834. Zbl0728.17010MR1082642
32. [Mal2] G. Maltsiniotis, Calcul différentiel sur le groupe linéaire quantique, Preprint (1990). 
33. [Mal3] G. Maltsiniotis, Groupoïdes quantiques, C.R.A.S.314, Sér. I (1992), 249-252. Zbl0767.17015MR1151708
34. [Mal4] G. Maltsiniotis, Le langage des espaces et des groupes quantiques, Preprint (1992). Zbl0783.17007MR1204772
35. [Man1] Yu. I. Manin, Some remarks on Koszul algebras and quantum groups, Ann. Inst. Fourier37, 4 (1987), 191-205. Zbl0625.58040MR927397
36. [Man2] Yu. I. Manin, "Quantum groups and non-commutative geometry," Centre de Recherches Mathématiques de l'Université de Montréal, 1988. Zbl0724.17006MR1016381
37. [Man3] Yu. I. Manin, Multiparametric quantum deformation of the general linear supergroup, Commun. Math. Phys.123 (1989), 163-175. Zbl0673.16004MR1002037
38. [Man4] Yu. I. Manin, Notes on quantum groups and quantum de Rham complexes, Preprint, MPI/91-60 (1991). Zbl0810.17003MR1119249
39. [MNW1] T. Masuda, Y. Nakagami, J. Watanabe, Noncommutative differential geometry on the quantum SU(2), I: An algebraic viewpoint, K-Theory4 (1990), 157-180. Zbl0719.46042MR1081658
40. [MNW2] T. Masuda, Y. Nakagami, J. Watanabe, Noncommutative differential geometry on the quantum two sphere of Podles, I: An algebraic viewpoint, K-Theory5 (1991), 151-175. Zbl0763.46059MR1140900
41. [M-H] F. Müller-Hoissen, Differential calculi on the quantum group $G{L}_{p,q}\left(2\right)$, Preprint, GOET-TP55/91 (1991). Zbl0764.17017
42. [NUW] M. Noumi, T. Umeda, M. Wakayama, A quantum analogue of the Capelli identity and an elementary differential calculus on $G{L}_q\left(n\right)$, Preprint, University of Tokyo (1991). Zbl0835.17013MR1302325
43. [Po] P. Podles, Differential calculus on quantum spheres, Lett. Math. Phys.18 (1989), 107-119. Zbl0702.53073MR1010990
44. [Pr] S. B. Priddy, Koszul resolutions, Trans. Amer. Math. Soc.152 (1970), 39-60. Zbl0261.18016MR265437
45. [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. Zbl0715.17015MR1015339
46. [Ro] M. Rosso, Algèbres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul différentiel non commutatif, Duke Math. J.61, 1 (1990), 11-40. Zbl0721.17013MR1068378
47. [Sch] A. Schirrmacher, Remarks on the use of R-matrices, Preprint (1991). Zbl0838.17016MR1205601
48. [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 Fields49 (1991), 317-324. MR1094112
49. [SVZ] W. B. Schmidke, S. P. Vokos, B. Zumino, Differential geometry of the quantum supergroup $G{L}_q\left(1\right|1)$, Z. Phys. C - Particles and Fields48 (1990), 249-255. Zbl0973.17504MR1076363
50. [Su] A. Sudbery, Consistent multiparameter quantisation of GL(n), J. Phys. A: Math. Gen.23 (1990), L697-L704. Zbl0722.17007MR1068228
51. [Ta] L. A. Takhtadzhyan, Noncommutative homology of quantum tori, Funct. Anal, and Appl.23, 2 (1989), 147-149. Zbl0708.19003MR1011367
52. [Tsy] B. Tsygan, Notes on differential forms on quantum groups, Preprint (1991). Zbl1013.58501MR1215528
53. [WZ] J. Wess, B. Zumino, Covariant differential calculus on the quantum hyperplane, Preprint (1990). Zbl0957.46514MR1128150
54. [Wo1] S. L. Woronowicz, Twisted SU(2) group. An example of a non-commutative differential calculus, Publ. RIMS23 (1987), 117-181. Zbl0676.46050MR890482
55. [Wo2] S. L. Woronowicz, Differential calculus on compact matrix pseudogroups (quantum groups), Commun. Math. Phys.122 (1989), 125-170. Zbl0751.58042MR994499
56. [Za1] S. Zakrzewski, A differential structure for quantum mechanics, J. of Geom. and Phys.2, 3 (1985), 135-145. Zbl0607.46041MR851125
57. [Za2] S. Zakrzewski, Quantum and classical pseudogroups. Part II. Differential and symplectic pseudogroups, Commun. Math. Phys.134 (1990), 371-395. Zbl0708.58031MR1081011