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Research Article | Open Access

Representation rings of extensions of Hopf algebra of Kac-Paljutkin type

Dong Su1, Shilin Yang2( )
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China
School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China
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Abstract

In this paper, we focus on studying two classes of finite dimensional Δ-associative algebras, which are extensions of a family of 2n2-dimensional Kac-Paljutkin type semi-simple Hopf algebras H2n2. All their indecomposable modules are classified. Furthermore, their representation rings are described by generators with suitable relations.

Keywords

Δ-associative algebratensor productrepresentation ring

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Electronic Research Archive
Volume 32 Issue 9,
September 2024
Pages 5201-5230
DOI: 10.3934/era.2024240

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Cite this article:
Su D, Yang S. Representation rings of extensions of Hopf algebra of Kac-Paljutkin type. Electronic Research Archive, 2024, 32(9): 5201-5230. https://doi.org/10.3934/era.2024240

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Received: 23 April 2024
Revised: 19 July 2024
Accepted: 29 August 2024
Published: 05 September 2024
©2024 the Author(s), licensee AIMS Press.

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