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Mathematics > Quantum Algebra

arXiv:1804.08973 (math)
[Submitted on 24 Apr 2018 (v1), last revised 27 Apr 2018 (this version, v2)]

Title:A classification result on prime Hopf algebras of GK-dimension one

Authors:Gongxiang Liu
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Abstract:In this paper, we classify all prime Hopf algebras $H$ of GK-dimension one satisfying the following two conditions: 1) $H$ has a 1-dimensional representation of order this http URL$(H)$ and 2) the invariant components of $H$ with respect to this 1-dimensional representation are domains (see Section 2 for related definitions). As consequences, 1) a number of new Hopf algebras of GK-dimension one are found and some of them are not pointed, 2) we give a partial answer to a question posed by Brown and Zhang and 3) some new kinds of finite-dimensional Hopf algebras are found.
Comments: 92 pages. In page 2, the graph should be "cusp $\in ^{\Z_6}_{Z_6}\mathcal{YD}$ ". Your comments are very welcome! Comparing with the first version, some typos were corrected
Subjects: Quantum Algebra (math.QA)
Cite as: arXiv:1804.08973 [math.QA]
  (or arXiv:1804.08973v2 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.1804.08973
Journal reference: Journal of Algebra, 547 (2020) 579-667

Submission history

From: Gongxiang Liu [view email]
[v1] Tue, 24 Apr 2018 12:06:28 UTC (64 KB)
[v2] Fri, 27 Apr 2018 08:14:02 UTC (64 KB)
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