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Research Article | Open Access

Projective class rings of a kind of category of Yetter-Drinfeld modules

Yaguo Guo, Shilin Yang( )
Faculty of Science, Beijing University of Technology, Beijing 100124, China
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Abstract

In this paper, all simple Yetter-Drinfeld modules and indecomposable projective Yetter-Drinfeld modules over a family of non-pointed 8 m-dimension Hopf algebras of tame type with rank two, are construted and classified. The technique is Radford's method of constructing Yetter-Drinfeld modules over a Hopf algebra. Furthermore, the projective class rings of the category of Yetter-Drinfeld modules over this class of Hopf algebras are described explicitly by generators and relations.

Keywords

simple subcomoduleYetter-Drinfeld moduletensor productthe projective class ring
CLC number: 16D70, 16T05, 16T99

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AIMS Mathematics
Volume 8 Issue 5,
May 2023
Pages 10997-11014
DOI: 10.3934/math.2023557

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Cite this article:
Guo Y, Yang S. Projective class rings of a kind of category of Yetter-Drinfeld modules. AIMS Mathematics, 2023, 8(5): 10997-11014. https://doi.org/10.3934/math.2023557

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Received: 13 January 2023
Revised: 14 February 2023
Accepted: 20 February 2023
Published: 15 May 2023
©2023 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)