La -matrice pour les algèbres quantiques de type affine non tordu
Annales scientifiques de l'École Normale Supérieure (1998)
- Volume: 31, Issue: 4, page 493-523
- ISSN: 0012-9593
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topDamiani, Ilaria. "La $R$-matrice pour les algèbres quantiques de type affine non tordu." Annales scientifiques de l'École Normale Supérieure 31.4 (1998): 493-523. <http://eudml.org/doc/82467>.
@article{Damiani1998,
author = {Damiani, Ilaria},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {simple Lie algebra; Kac-Moody algebra; quantum group; -matrix; Killing form; PBW basis},
language = {fre},
number = {4},
pages = {493-523},
publisher = {Elsevier},
title = {La $R$-matrice pour les algèbres quantiques de type affine non tordu},
url = {http://eudml.org/doc/82467},
volume = {31},
year = {1998},
}
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
PB - Elsevier
VL - 31
IS - 4
SP - 493
EP - 523
LA - fre
KW - simple Lie algebra; Kac-Moody algebra; quantum group; -matrix; Killing form; PBW basis
UR - http://eudml.org/doc/82467
ER -
References
top- [1] J. BECK, Braid group action and quantum affine algebras, (Commun. Math. Phys., vol. 165, 1994, p. 555-568). Zbl0807.17013MR95i:17011
- [2] J. BECK, Convex bases of PBW type for quantum affine algebras, (Commun. Math. Phys., vol. 165, 1994, p. 193-199). Zbl0828.17016MR96b:17008
- [3] N. BOURBAKI, Groupes et algèbres de Lie 4, 5, 6, Hermann, Paris, 1968.
- [4] I. DAMIANI, 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). Zbl0881.17012MR98b:17012
- [5] I. DAMIANI et C. DE CONCINI, Quantum groups and Poisson groups in (Baldoni-Picardello, Representations of Lie groups and quantum groups, Longman Scientific and Technical, 1994, p. 1-45). Zbl0828.17012MR97m:16070
- [6] C. DE CONCINI, V. G. KAC, Representations of quantum groups at roots of 1, (Progr. in Math., vol. 92, 1990, p. 471-506, Birkhäuser). Zbl0738.17008MR92g:17012
- [7] V. G. DRINFELD, A new realization of Yangians and quantized affine algebras, (Soviet Math. Dokl., vol. 36, 1988, n° 2, p. 212-216). Zbl0667.16004MR88j:17020
- [8] V. G. DRINFELD, Hopf algebras and quantum Yang-Baxter equation, (Soviet Math. Dokl., vol. 32, 1985, p. 254-258). Zbl0588.17015MR87h:58080
- [9] V. G. DRINFELD, Quantum groups, (Proc. ICM, Berkeley, 1986, p. 798-820). Zbl0667.16003MR89f:17017
- [10] J. E. HUMPHREYS, Introduction to Lie Algebras and Representation Theory, (Springer-Verlag, USA 1972). Zbl0254.17004MR48 #2197
- [11] M. JIMBO, A q-difference analogue of U(g) and the Yang-Baxter equation, (Lett. Math. Phys., vol. 10, 1985, p. 63-69). Zbl0587.17004MR86k:17008
- [12] V. G. KAC, Infinite Dimensional Lie Algebras, (Birkhäuser Boston, Inc., USA, 1983). Zbl0537.17001MR86h:17015
- [13] V. G. KAC et D. A. KAZHDAN, Structure of representations with highest weight of infinite-dimensional Lie algebras, (Adv. Math., vol. 34, 1979, p. 97-108). Zbl0427.17011MR81d:17004
- [14] S. M. KHOROSHKIN et V. N. TOLSTOY, Universal R-matrix for quantized(super) algebras, (Commun. Math. Phys., vol. 141, 1991, p. 599-617). Zbl0744.17015MR93a:16031
- [15] S. M. KHOROSHKIN et V. N. TOLSTOY, The universal R-matrix for quantum nontwisted affine Lie algebras, (Funkz. Analiz i ego pril., vol. 26:1, 1992, p. 85-88). Zbl0758.17011
- [16] A. N. KIRILLOV et N. RESHETIKHIN, q-Weyl Group and a Multiplicative Formula for Universal R-Matrices, (Commun. Math. Phys., vol. 134, 1990, p. 421-431). Zbl0723.17014MR92c:17023
- [17] S. Z. LEVENDORSKII et Ya. S. SOIBELMAN, 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). Zbl0729.17010MR93a:17017
- [18] S. Z. LEVENDORSKII et Ya. S. SOIBELMAN, Some applications of quantum Weyl group I, (J. Geom. Phys., vol. 7, 1990, p. 241-254). Zbl0729.17009MR92g:17016
- [19] S. Z. LEVENDORSKII, Ya. S. SOIBELMAN et V. STUKOPIN, 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). Zbl0776.17011MR94e:17021
- [20] G. LUSZTIG, Finite-dimensional Hopf algebras arising from quantum groups, (J. Amer. Math. Soc., vol. 3, 1990, p. 257-296). Zbl0695.16006MR91e:17009
- [21] G. LUSZTIG, Introduction to quantum groups, (Birkhäuser Boston, USA, 1993). Zbl0788.17010MR94m:17016
- [22] G. LUSZTIG, Quantum groups at roots of 1, (Geom. Ded., vol. 35, 1990, p. 89-113). Zbl0714.17013MR91j:17018
- [23] H. MATSUMOTO, Générateurs et relations des groupes de Weyl généralisés, (C. R. Acad. Sci. Paris, tome 258, Série II, 1964, p. 3419-3422). Zbl0128.25202MR32 #1294
- [24] M. ROSSO, An Analogue of P.B.W. Theorem and the Universal R-Matrix for Uhsl(N + 1), (Commun. Math. Phys., vol. 124, 1989, p. 307). Zbl0694.17006MR90h:17019
- [25] M. ROSSO, 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). Zbl0753.17027MR93i:17020
- [26] T. TANISAKI, 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). Zbl0870.17007MR93k:17040
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