The quasi-Hopf analogue of u_q(sl₂)

2012/02/08 by Gongxiang Liu, Liu, Gongxiang · 1 citation
Mathematics · #16W30 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1202.1631

openalex publication_date 2012/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [4], some quasi-Hopf algebras of dimension n³, 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 n³ constructed in [4] is always twist equivalent to Lusztig's small quantum group u_q(sl₂) if n is odd. Based on computations and analysis, we show that this is not the case if n is even. That is, the quasi-Hopf analogue Qu_q(sl₂) of u_q(sl₂) is gotten.

Cited by

• Representations of the small quasi-quantum group Qu_q(\mathfraksl₂)

Related

• Quasi-Hopf algebras associated with sl(2) and complex curves
• Doubles of Quasi-Quantum Groups
• Small quantum groups associated to Belavin-Drinfeld triples
• Drinfel'd twist of multiplier Hopf algebras
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