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Finite Dimensional Representations of Ut(sl (2)) at Roots of Unity

Published online by Cambridge University Press:  20 November 2018

Xiao Jie*
Affiliation:
Department of Mathematics, Beijing Normal University,Beijing 100875, People's Republic of China
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Abstract

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All finite dimensional indecomposable representations of Ut(Sl (2)) at roots of 1 are determined.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1997

References

[A] Alperin, J.L., Local representation theory, Cambridge University Press, 1986.Google Scholar
[APW] Andersen, H.H., Polo, P. and Wen, K., Representations of quantum algebras. Invent. Math. 104(1991), 159.Google Scholar
[AR] Auslander, M. and Reiten, I., Representation theory of artin algebras III: almost split sequences. Comm. Algebra 3(1975), 239294.Google Scholar
[BGG] Bernstein, J., Gelfand, I.M. and Gelfand, S.I., A category of G-modules. Functional Anal. Appl. 10(1976), 8792.Google Scholar
[DCK] De Concini, C. and Kac, V.G., Representations of quantum groups at roots of 1, Progr.Math. 92(1990), 471506.Google Scholar
[DR] Dlab, V. and Ringel, C.M., Indecomposable representations of graphs and algebras. Mem.Amer.Math. Soc. 173(1976).Google Scholar
[Dr1] Drinfeld, V.G., Hopf algebras and quantum Yang-Baxter equation. Soviet Math. Dokl. 32(1985), 254– 258.Google Scholar
[Dr2] Drinfeld, V.G., Quantum groups, Proc. ICM, Berkeley, 1986. 798820.Google Scholar
[G] Gabriel, P., Auslander-Reiten sequences and representation-finite algebras. Springer, Lecture Notes in Math. 831, 1980. 171.Google Scholar
[Ha] Happel, D., Triangulated categories in the representation theory of finite dimensional algebras. London Math. Soc. Lecture Note Ser. 119(1988).Google Scholar
[Ji] Jimbo, M., A q-difference analogue of V(G) and the Yang-Baxter equation. Lett. Math. Phys. 10(1985), 6369.Google Scholar
[KiR] Kirillov, A.N. and Reshetikhin, N.Yu., Representations of the algebras Uq(sl 2), q-orthogonal polynomials and invariants of links. Preprint LOMI (E) 9(1988).Google Scholar
[KM] Kirby, R. and Melvin, P., The 3-manifold invariants ofWitten and Reshetikhin-Turaev for. sl (2, C), Invent. Math. 105(1991), 473545.Google Scholar
[KR] Kulish, P.P. and Reshetikhin, N.Yu., J. Soviet Math. 23(1983), 2435.Google Scholar
[Lu] Lusztig, G., Quantum deformations of certain simple modules over enveloping algebras. Adv. Math. 70(1988), 237249.Google Scholar
[Ri] Ringel, C.M., Tame algebras and integral quadratic forms. Springer, Lecture Notes in Math. 1099, 1984.Google Scholar
[Ro] Rosso, M., Finite dimensional representations of the quantum analogue of the enveloping algebra of a complex simple Lie algebra. Comm. Math. Phys. 117(1988), 583593.Google Scholar
[RS] Rudakov, A.N. and Shafarevich, I.R., On the irreducible representations of a simple three-dimensional Lie algebra over a field of finite characteristic. Math. Notes 2(1967), 439454.Google Scholar
[RT1] Reshetikhin, N.Yu. and Turaev, V.G., Ribbon graphs and their invariants derived from quantum groups. Comm. Math. Phys. 127(1990), 126.Google Scholar
[RT2] Reshetikhin, N.Yu., Invariants of 3-manifolds via link polynomials and quantum groups. Invent. Math. 103(1991), 547597.Google Scholar
[Ru] Rudakov, A.N., Reducible P-representations of a simple three-dimensional Lie P-algebra. Moscow Univ. Math. Bull. 37(1982), 5156.Google Scholar
[Su] Suter, R., Modules over Uq. (sl2), Comm. Math. Phys. 163(1994), 359393.Google Scholar
[X1] Xiao, J., Generic modules over the quantum group Ut(sl(2)) at t a root of unity. Manuscripta Math. 83(1994), 7598.Google Scholar
[X2] Xiao, J., Restricted representations of U(sl(2))-quantizations. Algebra Colloq. (1) 1(1994), 5666.Google Scholar
[XV] Xiao, J. and Van Oystaeyen, F., Weight modules and their extensions over a class of algebras similar to. the enveloping algebra of sl (2, C), J. Algebra 175(1995), 844864.Google Scholar