On the structure of irreducible Yetter-Drinfeld modules over D

A class of algebras $ D(m, d, \xi) $ introduced by <sup>[<span class="xref"><a href="#b22" ref-type="bibr">22</a></span>]</sup> were not pointed and generated by the coradical of $ D(m, d, \xi) $. Let $ D $ be the quotient of $ D(m, d...

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Bibliographic Details
Published in:AIMS Mathematics
Main Author: Yiwei Zheng
Format: Article
Language:English
Published: AIMS Press 2024-07-01
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Online Access:https://www.aimspress.com/article/doi/10.3934/math.20241035?viewType=HTML
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Summary:A class of algebras $ D(m, d, \xi) $ introduced by <sup>[<span class="xref"><a href="#b22" ref-type="bibr">22</a></span>]</sup> were not pointed and generated by the coradical of $ D(m, d, \xi) $. Let $ D $ be the quotient of $ D(m, d, \xi) $ module the principle ideal $ (g^m-1) $. First, we describe all simple left modules of $ D $. Then, according to Radford's method, we construct the Yetter-Drinfeld module over $ D $ by the tensor product of a simple module of $ D $ and $ D $ itself. Hence, we find some simple left Yetter-Drinfeld modules over $ D $, and the relevant braidings are of a triangular type.
ISSN:2473-6988