The quasi-Hopf analogue of $u_q(sl_2)$

Gongxiang Liu

paper

The quasi-Hopf analogue of $u_{q} (s l_{2})$

arXiv:1202.1631

Abstract

In [4], some quasi-Hopf algebras of dimension $n^{3}$ , which can be understood as the quasi-Hopf analogues of Taft algebras, are constructed. Moreover, the quasi-Hopf analogues of generalized Taft algebras are considered in [7], where the language of the dual of a quasi-Hopf algebra is used. The Drinfeld doubles of such quasi-Hopf algebras are computed in this paper. The authors in [5] shew that the Drinfeld double of a quasi-Hopf algebra of dimension $n^{3}$ constructed in [4] is always twist equivalent to Lusztig's small quantum group $u_{q} (s l_{2})$ if $n$ is odd. Based on computations and analysis, we show that this is \emph{not} the case if $n$ is even. That is, the quasi-Hopf analogue $Q u_{q} (s l_{2})$ of $u_{q} (s l_{2})$ is gotten.

19 pages

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The quasi-Hopf analogue of $u_{q} (s l_{2})$