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december 2016 Representations of the small quasi-quantum group ${\operatorname{Q}}\mathbf{u}_{q}(\mathfrak{sl}_{2})$
Gongxiang Liu, Fred Van Oystaeyen, Yinhuo Zhang
Bull. Belg. Math. Soc. Simon Stevin 23(5): 779-800 (december 2016). DOI: 10.36045/bbms/1483671626

Abstract

The quasi-Frobenius-Lusztig kernel ${\operatorname{Q}}\mathbf{u}_{q}(\mathfrak{sl}_{2})$ associated with $\mathfrak{sl}_{2}$ has been constructed in [9]. In this paper we study the representations of this small quasi-quantum group. We give a complete list of non-isomorphic indecomposables and the tensor product decomposition rules for simples and projectives. A description of the Grothendieck ring is also provided.

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Gongxiang Liu. Fred Van Oystaeyen. Yinhuo Zhang. "Representations of the small quasi-quantum group ${\operatorname{Q}}\mathbf{u}_{q}(\mathfrak{sl}_{2})$." Bull. Belg. Math. Soc. Simon Stevin 23 (5) 779 - 800, december 2016. https://doi.org/10.36045/bbms/1483671626

Information

Published: december 2016
First available in Project Euclid: 6 January 2017

zbMATH: 1364.17020
MathSciNet: MR3593575
Digital Object Identifier: 10.36045/bbms/1483671626

Subjects:
Primary: 16G10 , 16T20

Keywords: Frobenius-Lusztig kernel , genuine quasi-Hopf algebra , Quasi-Hopf algebra

Rights: Copyright © 2016 The Belgian Mathematical Society

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Vol.23 • No. 5 • december 2016
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