@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, Tome 43 (1992), Exposé no. 9, 18 p. http://archive.numdam.org/item/RCP25_1992__43__163_0/
[Ab] Hopf algebras," Cambridge Tracts in Math. 74, Cambridge Univ. Press, 1980. | MR | Zbl
, "[Ao1] q-analogue of the de Rham cohomology associated with Jackson integrals. I, Proc. Japan Acad. 66 (A) (1990), 161-164. | MR | Zbl
,[Ao2] q-analogue of the de Rham cohomology associated with Jackson integrals. II, Proc. Japan Acad. 66 (A) (1990), 240-244. | MR | Zbl
,[Ao3] Finiteness of a cohomology associated with certain Jackson integrals, Tôhoku Math. J. 43 (1991), 75-101. | MR | Zbl
,[AST] Quantum deformations of GLn, Comm. Pure Appl. Math. 44 (1991), 879-895. | MR | Zbl
, , ,[Be] The diamond lemma for ring theory, Adv. Math. 29 (1978), 178-218. | MR | Zbl
,[Bd] Quantum Lie algebras and differential calculus on quantum groups, Preprint (1990). | MR | Zbl
,[Bo] Eléments de Mathématique," Algèbre, Chapitres 1 à 3, Hermann, Paris, 1970. | Zbl
, "[Br] Exterior bialgebras, Preprint (1991).
,[BDR] On the quantum differential calculus and the quantum holomorphicity, J. Math. Phys. 33, 1 (1992), 19-24. | MR | Zbl
, , ,[CSWW] Bicovariant differential calculus on quantum groups SUq(N) and SOq(N), Commun. Math. Phys. 142 (1991), 605-641. | MR | Zbl
, , , ,[Ca] Calcul différentiel non commutatif, Exposés à l'E.N.S. (1989).
,[Co] Non-commutative differential geometry, Publications Mathématiques de l'I.H.E.S. 62 (1985), 41-144. | EuDML | Numdam | Zbl
,[DM] Tannakian categories, in "Hodge cycles, motives, and Shimura varieties," Lecture Notes in Mathematics 900, Springer-Verlag, 1982, pp. 101-228. | MR | Zbl
, ,[Dr] Quantum groups, in "Proceedings of the International Congress of Mathematicians 1986, Berkeley," AMS, 1987, pp. 798-820. | MR | Zbl
,[DV1] Dérivations et calcul différentiel non commutatif, C.R.A.S. 307 (1988), 403-408. | MR | Zbl
,[DV2] Noncommutative differential geometry, quantum mechanics and gauge theory, Preprint, L.P.T.H.E.-Orsay 90/31 (1990). | MR | Zbl
,[DKM1] Noncommutative differential geometry of matrix algebras, J. Math. Phys. 31, 2 (1990), 316-322. | MR | Zbl
, , ,[DKM2] Noncommutative differential geometry and new models of gauge theory, J. Math. Phys. 31, 2 (1990), 323-330. | MR | Zbl
, , ,[FT] Hochschild and cyclic homology of quantum groups, Commun. Math. Phys. 140 (1991), 481-521. | MR | Zbl
, ,[EGA IV4] Éléments de géométrie algébrique IV," Publications Mathématiques de l'I.H.E.S. 32, 1967. | Numdam | Zbl
, "[Gr] 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] Non-commutative differential geometry and Yang-Baxter equation, Preprint (1990). | Zbl
, , ,[HW] A q-analogue of Capelli's identity for GL(2), Preprint, Hokkaido University (1991). | MR | Zbl
, ,[J1] A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), 63-69. | MR | Zbl
,[J2] Quantum R matrix for the generalized Toda system, Commun. Math. Phys. 102 (1986), 537-547. | MR | Zbl
,[J3] 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] Lett. Math. Phys. 22 (1991), 177-186. | MR | Zbl
, ,[Ka] Homologie cyclique et K-théorie," Asterisque 149, 1987. | Numdam | MR | Zbl
, "[Kas] Cyclic homology of differential operators, the Virasoro algebra and a q-analogue, Preprint (1991). | MR | Zbl
,[Mal1] Groupes quantiques et structures différentielles, C.R.A.S. 311, Sér. I (1990), 831-834. | MR | Zbl
,[Mal2] Calcul différentiel sur le groupe linéaire quantique, Preprint (1990).
,[Mal3] Groupoïdes quantiques, C.R.A.S. 314, Sér. I (1992), 249-252. | MR | Zbl
,[Mal4] Le langage des espaces et des groupes quantiques, Preprint (1992). | MR | Zbl
,[Man1] Some remarks on Koszul algebras and quantum groups, Ann. Inst. Fourier 37, 4 (1987), 191-205. | EuDML | Numdam | MR | Zbl
,[Man2] Quantum groups and non-commutative geometry," Centre de Recherches Mathématiques de l'Université de Montréal, 1988. | MR | Zbl
, "[Man3] Multiparametric quantum deformation of the general linear supergroup, Commun. Math. Phys. 123 (1989), 163-175. | MR | Zbl
,[Man4] Notes on quantum groups and quantum de Rham complexes, Preprint, MPI/91-60 (1991). | MR | Zbl
,[MNW1] Noncommutative differential geometry on the quantum SU(2), I: An algebraic viewpoint, K-Theory 4 (1990), 157-180. | MR | Zbl
, , ,[MNW2] Noncommutative differential geometry on the quantum two sphere of Podles, I: An algebraic viewpoint, K-Theory 5 (1991), 151-175. | MR | Zbl
, , ,[M-H] Differential calculi on the quantum group , Preprint, GOET-TP55/91 (1991). | Zbl
,[NUW] A quantum analogue of the Capelli identity and an elementary differential calculus on , Preprint, University of Tokyo (1991). | MR | Zbl
, , ,[Po] Differential calculus on quantum spheres, Lett. Math. Phys. 18 (1989), 107-119. | MR | Zbl
,[Pr] Koszul resolutions, Trans. Amer. Math. Soc. 152 (1970), 39-60. | MR | Zbl
,[RTF] Quantization of Lie groups and Lie algebras, Len. Math. J. 1, 1 (1990), 193-225. | MR | Zbl
, , ,[Ro] Algèbres enveloppantes quantifiées, groupes quantiques compacts de matrices et calcul différentiel non commutatif, Duke Math. J. 61, 1 (1990), 11-40. | MR | Zbl
,[Sch] Remarks on the use of R-matrices, Preprint (1991). | MR | Zbl
,[SWZ] 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] Differential geometry of the quantum supergroup , Z. Phys. C - Particles and Fields 48 (1990), 249-255. | MR | Zbl
, , ,[Su] Consistent multiparameter quantisation of GL(n), J. Phys. A: Math. Gen. 23 (1990), L697-L704. | MR | Zbl
,[Ta] Noncommutative homology of quantum tori, Funct. Anal, and Appl. 23, 2 (1989), 147-149. | MR | Zbl
,[Tsy] Notes on differential forms on quantum groups, Preprint (1991). | MR | Zbl
,[WZ] Covariant differential calculus on the quantum hyperplane, Preprint (1990). | MR | Zbl
, ,[Wo1] Twisted SU(2) group. An example of a non-commutative differential calculus, Publ. RIMS 23 (1987), 117-181. | MR | Zbl
,[Wo2] Differential calculus on compact matrix pseudogroups (quantum groups), Commun. Math. Phys. 122 (1989), 125-170. | MR | Zbl
,[Za1] A differential structure for quantum mechanics, J. of Geom. and Phys. 2, 3 (1985), 135-145. | MR | Zbl
,[Za2] Quantum and classical pseudogroups. Part II. Differential and symplectic pseudogroups, Commun. Math. Phys. 134 (1990), 371-395. | MR | Zbl
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