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EXTENDED QUANTUM ENVELOPING ALGEBRAS OF (2)

Published online by Cambridge University Press:  01 September 2009

WU ZHIXIANG
WU ZHIXIANG*
Affiliation:
Mathematics Department, Zhejiang University, Hangzhou 310027, P.R. China e-mail: [email protected]
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Abstract

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In present paper we define a new kind of quantized enveloping algebra of (2). We denote this algebra by Ur,t, where r, t are two non-negative integers. It is a non-commutative and non-cocommutative Hopf algebra. If r = 0, then the algebra Ur,t is isomorphic to a tensor product of the algebra of infinite cyclic group and the usual quantum enveloping algebra of (2) as Hopf algebras. The representation of this algebra is studied.

Keywords

Primary 17B67Secondary 17B10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 3 , September 2009 , pp. 441 - 465
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Drinfeld, V. G., Hopf algebras and the quantum Yang–Baxter equation, Sov. Math. Dokl. 32 (1985), 254–258.Google Scholar
2.Frankel, I., Khovanov, M. and Stroppel, C., A categorification of finite-dimensional irreducible representations of quantum 2 and their tensor products, Selecta Math. 12 (3–4) (2006), 379–431.CrossRefGoogle Scholar
3.Jimbo, M., A q-difference analogue of U() and the Yang–Baxter equation, Lett. Math. Phys. 10 (1985), 63–69.CrossRefGoogle Scholar
4.Kac, V. G., Infinite dimensional Lie algebras, 3rd edition (Cambridge University Press, Cambridge, 1990).CrossRefGoogle Scholar
5.Lusztig, G., Introduction to quantum group (Birkhäuser, Boston, 1993).Google Scholar
6.Rosso, M., Finite-dimensional representations of the quantum analog of enveloping algebra of a complex simple Lie algebra, Comm. Math. Phys. 117 (1998), 581–593.CrossRefGoogle Scholar
7.Savage, A., The tensor product of representations of Uq(2) via quivers, Adv. Math. 177 (2) (2003), 297–340.Google Scholar
8.Siu-Hung, Ng., Hopf algebras of dimension pq, J. Algebra 319 (7) (2008), 2772–2788.Google Scholar
9.Tanisaki, T., Harish-Chandra isomorphisms for quantum algebras, Comm. Math. Phys. 127 (1990), 555–571.CrossRefGoogle Scholar
10.Vivek, Y. and Savasvati, Y., On the models of certain p, q-algebra representations: The p, q-oscillator algebra, J. Math. Phys. 49 (5) (2008), 053504, 1–12.Google Scholar
11.Zhixiang, Wu, A class of weak Hopf algebras related to a Borcherds-Cartan Matrix, J. Phys. A Math. gen. 39 (2006), 14611–14626.CrossRefGoogle Scholar