@article{ASENS_1998_4_31_4_493_0, author = {Damiani, Ilaria}, title = {La $R$-matrice pour les alg\`ebres quantiques de type affine non tordu}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {493--523}, publisher = {Elsevier}, volume = {4e s{\'e}rie, 31}, number = {4}, year = {1998}, doi = {10.1016/s0012-9593(98)80104-3}, mrnumber = {99g:17027}, zbl = {0911.17005}, language = {fr}, url = {http://www.numdam.org/articles/10.1016/s0012-9593(98)80104-3/} }
TY - JOUR AU - Damiani, Ilaria TI - La $R$-matrice pour les algèbres quantiques de type affine non tordu JO - Annales scientifiques de l'École Normale Supérieure PY - 1998 SP - 493 EP - 523 VL - 31 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/s0012-9593(98)80104-3/ DO - 10.1016/s0012-9593(98)80104-3 LA - fr ID - ASENS_1998_4_31_4_493_0 ER -
%0 Journal Article %A Damiani, Ilaria %T La $R$-matrice pour les algèbres quantiques de type affine non tordu %J Annales scientifiques de l'École Normale Supérieure %D 1998 %P 493-523 %V 31 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/s0012-9593(98)80104-3/ %R 10.1016/s0012-9593(98)80104-3 %G fr %F ASENS_1998_4_31_4_493_0
Damiani, Ilaria. La $R$-matrice pour les algèbres quantiques de type affine non tordu. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 31 (1998) no. 4, pp. 493-523. doi : 10.1016/s0012-9593(98)80104-3. http://www.numdam.org/articles/10.1016/s0012-9593(98)80104-3/
[1] Braid group action and quantum affine algebras, (Commun. Math. Phys., vol. 165, 1994, p. 555-568). | MR | Zbl
,[2] Convex bases of PBW type for quantum affine algebras, (Commun. Math. Phys., vol. 165, 1994, p. 193-199). | MR | Zbl
,[3] Groupes et algèbres de Lie 4, 5, 6, Hermann, Paris, 1968.
,[4] The Highest Coefficient of detHη and the Center of the Specialization at Odd Roots of Unity for Untwisted Affine Quantum Algebras, (J. Algebra, vol. 186, 1996, p. 736-780). | MR | Zbl
,[5] Quantum groups and Poisson groups in (Baldoni-Picardello, Representations of Lie groups and quantum groups, Longman Scientific and Technical, 1994, p. 1-45). | MR | Zbl
et ,[6] Representations of quantum groups at roots of 1, (Progr. in Math., vol. 92, 1990, p. 471-506, Birkhäuser). | MR | Zbl
, ,[7] A new realization of Yangians and quantized affine algebras, (Soviet Math. Dokl., vol. 36, 1988, n° 2, p. 212-216). | MR | Zbl
,[8] Hopf algebras and quantum Yang-Baxter equation, (Soviet Math. Dokl., vol. 32, 1985, p. 254-258). | MR | Zbl
,[9] Quantum groups, (Proc. ICM, Berkeley, 1986, p. 798-820). | MR | Zbl
,[10] Introduction to Lie Algebras and Representation Theory, (Springer-Verlag, USA 1972). | MR | Zbl
,[11] A q-difference analogue of U(g) and the Yang-Baxter equation, (Lett. Math. Phys., vol. 10, 1985, p. 63-69). | MR | Zbl
,[12] Infinite Dimensional Lie Algebras, (Birkhäuser Boston, Inc., USA, 1983). | MR | Zbl
,[13] Structure of representations with highest weight of infinite-dimensional Lie algebras, (Adv. Math., vol. 34, 1979, p. 97-108). | MR | Zbl
et ,[14] Universal R-matrix for quantized(super) algebras, (Commun. Math. Phys., vol. 141, 1991, p. 599-617). | MR | Zbl
et ,[15] The universal R-matrix for quantum nontwisted affine Lie algebras, (Funkz. Analiz i ego pril., vol. 26:1, 1992, p. 85-88). | Zbl
et ,[16] q-Weyl Group and a Multiplicative Formula for Universal R-Matrices, (Commun. Math. Phys., vol. 134, 1990, p. 421-431). | MR | Zbl
et ,[17] Quantum Weyl group and multiplicative formula for the R-matrix of a simple Lie algebra, (Funct. Analysis and its Appl., 2 vol. 25, 1991, p. 143-145). | MR | Zbl
et ,[18] Some applications of quantum Weyl group I, (J. Geom. Phys., vol. 7, 1990, p. 241-254). | MR | Zbl
et ,[19] The Quantum Weyl Group and the Universal Quantum R-Matrix for Affine Lie Algebra A(1)1, (Lett. Math. Phys., vol. 27, 1993, p. 253-264). | MR | Zbl
, et ,[20] Finite-dimensional Hopf algebras arising from quantum groups, (J. Amer. Math. Soc., vol. 3, 1990, p. 257-296). | MR | Zbl
,[21] Introduction to quantum groups, (Birkhäuser Boston, USA, 1993). | MR | Zbl
,[22] Quantum groups at roots of 1, (Geom. Ded., vol. 35, 1990, p. 89-113). | MR | Zbl
,[23] Générateurs et relations des groupes de Weyl généralisés, (C. R. Acad. Sci. Paris, tome 258, Série II, 1964, p. 3419-3422). | MR | Zbl
,[24] An Analogue of P.B.W. Theorem and the Universal R-Matrix for Uhsl(N + 1), (Commun. Math. Phys., vol. 124, 1989, p. 307). | MR | Zbl
,[25] Certaines formes bilinéaires sur les groupes quantiques et une conjecture de Schechtman et Varchenko, (C. R. Acad. Sci. Paris, tome 314, Série I, 1992, p. 5-8). | MR | Zbl
,[26] Killing forms, Harish-Chandra isomorphisms and universal R-matrices for Quantum Algebras, in (Infinite Analysis Part B, Adv. Series in Math. Phys., vol. 16, 1992, p. 941-962). | MR | Zbl
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