Tensor structures arising from affine Lie algebras. IV

Kazhdan, D.; Lusztig, G.

doi:10.1090/S0894-0347-1994-1239507-1

Tensor structures arising from affine Lie algebras. IV
HTML articles powered by AMS MathViewer

by D. Kazhdan and G. Lusztig

J. Amer. Math. Soc. 7 (1994), 383-453

DOI: https://doi.org/10.1090/S0894-0347-1994-1239507-1

PDF | Request permission

Part I: J. Amer. Math. Soc. (1993), 905-947
Part II: J. Amer. Math. Soc. (1993), 949-1011
Part III: J. Amer. Math. Soc. (1994), 335-381

References

Henning Haahr Andersen, Patrick Polo, and Ke Xin Wen, Representations of quantum algebras, Invent. Math. 104 (1991), no. 1, 1–59. MR 1094046, DOI 10.1007/BF01245066
Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
V. G. Drinfel′d, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with $\textrm {Gal}(\overline \textbf {Q}/\textbf {Q})$, Algebra i Analiz 2 (1990), no. 4, 149–181 (Russian); English transl., Leningrad Math. J. 2 (1991), no. 4, 829–860. MR 1080203
V. G. Drinfel′d, Almost cocommutative Hopf algebras, Algebra i Analiz 1 (1989), no. 2, 30–46 (Russian); English transl., Leningrad Math. J. 1 (1990), no. 2, 321–342. MR 1025154

Quantum groups

Jens C. Jantzen, Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren, Math. Ann. 226 (1977), no. 1, 53–65. MR 439902, DOI 10.1007/BF01391218
André Joyal and Ross Street, The geometry of tensor calculus. I, Adv. Math. 88 (1991), no. 1, 55–112. MR 1113284, DOI 10.1016/0001-8708(91)90003-P
V. G. Kac and D. A. Kazhdan, Structure of representations with highest weight of infinite-dimensional Lie algebras, Adv. in Math. 34 (1979), no. 1, 97–108. MR 547842, DOI 10.1016/0001-8708(79)90066-5
George Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston, Inc., Boston, MA, 1993. MR 1227098
G. Lusztig, Modular representations and quantum groups, Classical groups and related topics (Beijing, 1987) Contemp. Math., vol. 82, Amer. Math. Soc., Providence, RI, 1989, pp. 59–77. MR 982278, DOI 10.1090/conm/082/982278
George Lusztig, On quantum groups, J. Algebra 131 (1990), no. 2, 466–475. MR 1058558, DOI 10.1016/0021-8693(90)90187-S
Saunders MacLane, Categories for the working mathematician, Graduate Texts in Mathematics, Vol. 5, Springer-Verlag, New York-Berlin, 1971. MR 0354798
Claus Michael Ringel, The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences, Math. Z. 208 (1991), no. 2, 209–223. MR 1128706, DOI 10.1007/BF02571521
D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras. I, II, J. Amer. Math. Soc. 6 (1993), no. 4, 905–947, 949–1011. MR 1186962, DOI 10.1090/S0894-0347-1993-99999-X

Tensor structures arising from affine Lie algebras

6

D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras. III, J. Amer. Math. Soc. 7 (1994), no. 2, 335–381. MR 1239506, DOI 10.1090/S0894-0347-1994-1239506-X