EXTENDED QUANTUM ENVELOPING ALGEBRAS OF (2)
Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 441-465

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.1017/S0017089509005096
Mots-clés : Primary 17B67, Secondary 17B10
ZHIXIANG, WU. EXTENDED QUANTUM ENVELOPING ALGEBRAS OF (2). Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 441-465. doi: 10.1017/S0017089509005096
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[1] 1.Drinfeld, V. G., Hopf algebras and the quantum Yang–Baxter equation, Sov. Math. Dokl. 32 (1985), 254–258. Google Scholar

[2] 2.Frankel, I., Khovanov, M. and Stroppel, C., A categorification of finite-dimensional irreducible representations of quantum and their tensor products, Selecta Math. 12 (3–4) (2006), 379–431. Google Scholar | DOI

[3] 3.Jimbo, M., A q-difference analogue of U() and the Yang–Baxter equation, Lett. Math. Phys. 10 (1985), 63–69. Google Scholar | DOI

[4] 4.Kac, V. G., Infinite dimensional Lie algebras, 3rd edition (Cambridge University Press, Cambridge, 1990). Google Scholar | DOI

[5] 5.Lusztig, G., Introduction to quantum group (Birkhäuser, Boston, 1993). Google Scholar

[6] 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. Google Scholar | DOI

[7] 7.Savage, A., The tensor product of representations of U() via quivers, Adv. Math. 177 (2) (2003), 297–340. Google Scholar

[8] 8.Siu-Hung, Ng., Hopf algebras of dimension pq, J. Algebra 319 (7) (2008), 2772–2788. Google Scholar

[9] 9.Tanisaki, T., Harish-Chandra isomorphisms for quantum algebras, Comm. Math. Phys. 127 (1990), 555–571. Google Scholar | DOI

[10] 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] 11.Zhixiang, Wu, A class of weak Hopf algebras related to a Borcherds-Cartan Matrix, J. Phys. A Math. gen. 39 (2006), 14611–14626. Google Scholar | DOI

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