Representations of the small quasi-quantum group ${Q}\mathbf{u}_{q}(\mathfrak{sl}_{2})$

Gongxiang Liu; Fred Van Oystaeyen; Yinhuo Zhang

Representations of the small quasi-quantum group ${Q}\mathbf{u}_{q}(\mathfrak{sl}_{2})$

Quantum Algebra 2014-01-28 v1 Representation Theory

Authors: Gongxiang Liu , Fred Van Oystaeyen , Yinhuo Zhang

Abstract

The quasi-Frobenius-Lusztig kernel ${Q}\mathbf{u}_{q}(\mathfrak{sl}_{2})$ associated with $\mathfrak{sl}_{2}$ has been constructed in \cite{Liu}. 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 provided.

Keywords

quantum group representations quantum groups quasi-isometry

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@article{arxiv.1401.6843,
  title  = {Representations of the small quasi-quantum group ${Q}\mathbf{u}_{q}(\mathfrak{sl}_{2})$},
  author = {Gongxiang Liu and Fred Van Oystaeyen and Yinhuo Zhang},
  journal= {arXiv preprint arXiv:1401.6843},
  year   = {2014}
}

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19 pages, 9 fiqures

Representations of the small quasi-quantum group ${Q}\mathbf{u}_{q}(\mathfrak{sl}_{2})$

Abstract

Keywords

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