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Research Article | Open Access

On the structure of irreducible Yetter-Drinfeld modules over D

School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
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Abstract

A class of algebras D(m,d,ξ) introduced by [22] were not pointed and generated by the coradical of D(m,d,ξ). Let D be the quotient of D(m,d,ξ) module the principle ideal (gm−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.

Keywords

Yetter-Drinfeld moduleHopf algebra
CLC number: 16T05, 16T99

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 21321-21336
DOI: 10.3934/math.20241035

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Zheng Y. On the structure of irreducible Yetter-Drinfeld modules over D. AIMS Mathematics, 2024, 9(8): 21321-21336. https://doi.org/10.3934/math.20241035

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Received: 14 May 2024
Revised: 13 June 2024
Accepted: 18 June 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)