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Cohomology of Quantum Groups: the Quantum Dimension

Published online by Cambridge University Press:  20 November 2018

Brian Parshall  and
Jian-Pan Wang
Brian Parshall
Affiliation:
Department of Mathematics University of Virginia Charlottesville, Virginia 22903-3199 U.S.A.
Jian-Pan Wang
Affiliation:
Department of Mathematics East China Normal University Shanghai 200062 The People's Republic of China
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Abstract

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This paper uses the notion of the quantum dimension to obtain new results on the cohomology and representation theory of quantum groups at a root of unity. In particular, we consider the elementary theory of support varieties for quantum groups.

Keywords

20G1517B37
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 6 , 01 December 1993 , pp. 1276 - 1298
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Andersen, H.H., Tensor products of quantized tilting modules, Commun. Math. Phys. 149(1992), 149–159.Google Scholar
2. Andersen, H.H. and Jantzen, J.C., Cohomology of induced representations for algebraic groups, Math. Ann. 269(1984), 487–525.Google Scholar
3. Andersen, H.H., Polo, P. and Wen, K., Representations of quantum algebras, Invent, math. 104(1991), 1–59.Google Scholar
4. Andersen, H.H., Injective modules for quantum algebras, Amer. Jour. Math. 114(1992), 571–604.Google Scholar
5. Cline, E., Parshall, B. and Scott, L., Finite dimensional algebras and highest weight categories, J. Reine Angew. Math. 391(1988), 85–99.Google Scholar
6. Drinfel, V.G.'d, On almost cocommutative Hopf algebras, Leningrad Math. J. 1(1990), 321–342.Google Scholar
7. Friedlander, E. and Parshall, B., Geometry of p-unipotent Lie algebras, J. Algebra 109(1987), 25–45.Google Scholar
8. Friedlander, E., Support varieties for restricted Lie algebras, Invent, math. 86(1986), 553–562.Google Scholar
9. Fuchs, J., Affine Lie Algebras and Quantum Groups, Cambridge University Press, 1992.Google Scholar
10. Ginzberg, V. and Kumar, S., Cohomology of quantum groups at roots of unity, Duke Math. J. 69(1993), 179–198.Google Scholar
11. Hayashi, T., Quantum deformation of classical groups, Publ. RIMS, Kyoto Univ. 28(1992), 57–81.Google Scholar
12. Humphreys, J.E., Reflection Groups and Coxeter Groups, Cambridge studies in advanced mathematics (29), Cambridge University Press, 1990.Google Scholar
13. Janiszczak, I. and Jantzen, J.C., Simple periodic modules over Chevalley groups, J. London Math. Soc. (2) 41(1990), 217–230.Google Scholar
14. Janiszczak, I. and Jantzen, J.C., Kohomologie von p-Lie-Algebren und nilpotente Elemente, Abh. Math. Sem. Univ. Hamberg 56(1986), 191–219.Google Scholar
15. Janiszczak, I. and Jantzen, J.C., Restricted Lie algebra cohomology, Algebraic Groups: Proceedings of a Symposium in Honor of T.A. Springer, Springer-Verlag, 1987.91-108.Google Scholar
16. Janiszczak, I. and Jantzen, J.C., Support varieties ofWeyl modules, Bull. London Math. Soc. 19(1987), 238–244.Google Scholar
17. Janiszczak, I. and Jantzen, J.C., Representations of Algebraic Groups, Academic Press, 1987.Google Scholar
18. Kac, V.G., Infinite Dimensional Lie Algebras, Cambridge Univ. Press, 1990.Google Scholar
19. Kazhdan, D. and Lusztig, G., Affine Lie algebras and quantum groups, International Math. Res. Notices, Duke Math. J. 2(1991), 21–29.Google Scholar
20. Lusztig, G., Introduction to quantized enveloping algebras, In: New Developments in Lie Theory and Their Applications, (eds. Tirao, J. and Wallach, N.), Birkhauser, 1992.49-66.Google Scholar
21. Parshall, B. and J.-p. Wang, Quantum linear groups, Memoirs A.M.S. (439), 1991.Google Scholar
22. Parshall, B., Cohomology of infinitesimal quantum groups, I, Tôhoku Math. J. 44(1992), 395–423.Google Scholar