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

Authors: D. Kazhdan and G. Lusztig
Journal: J. Amer. Math. Soc. 7 (1994), 383-453
MSC: Primary 17B67
DOI: https://doi.org/10.1090/S0894-0347-1994-1239507-1
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
MathSciNet review: 1239507
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[APW] Henning Haahr Andersen, Patrick Polo, and Ke Xin Wen, Representations of quantum algebras, Invent. Math. 104 (1991), no. 1, 1–59. MR 1094046, https://doi.org/10.1007/BF01245066
[B] Hyman Bass, Algebraic 𝐾-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
[CE] Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
[D1] V. G. Drinfel′d, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with 𝐺𝑎𝑙(\overline{𝑄}/𝑄), Algebra i Analiz 2 (1990), no. 4, 149–181 (Russian); English transl., Leningrad Math. J. 2 (1991), no. 4, 829–860. MR 1080203
[D2] 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
[D3] -, Quantum groups, Proc. Internat. Congr. Math. (Berkeley, 1986), Amer. Math. Soc., Providence, RI, 1987, pp. 798-820.
[J] Jens C. Jantzen, Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren, Math. Ann. 226 (1977), no. 1, 53–65. MR 439902, https://doi.org/10.1007/BF01391218
[JS] André Joyal and Ross Street, The geometry of tensor calculus. I, Adv. Math. 88 (1991), no. 1, 55–112. MR 1113284, https://doi.org/10.1016/0001-8708(91)90003-P
[KK] 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, https://doi.org/10.1016/0001-8708(79)90066-5
[L] George Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston, Inc., Boston, MA, 1993. MR 1227098
[L1] 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, https://doi.org/10.1090/conm/082/982278
[L2] George Lusztig, On quantum groups, J. Algebra 131 (1990), no. 2, 466–475. MR 1058558, https://doi.org/10.1016/0021-8693(90)90187-S
[M] Saunders MacLane, Categories for the working mathematician, Springer-Verlag, New York-Berlin, 1971. Graduate Texts in Mathematics, Vol. 5. MR 0354798
[R] 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, https://doi.org/10.1007/BF02571521
[1] 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, https://doi.org/10.1090/S0894-0347-1993-1186962-0
[2] -, Tensor structures arising from affine Lie algebras. II, J. Amer. Math. Soc. 6 (1993), 949-1011.
[3] 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, https://doi.org/10.1090/S0894-0347-1994-1239506-X