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Research Article | Open Access

The criteria for automorphisms on finite-dimensional algebras

Yanni Yang1,2, Quanguo Chen1( )
College of Mathematics and Statistics, Kashi University, Kashi 844000, China
School of Mathematical science, Nankai University, Tianjin 300071, China
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Abstract

In this paper, we will establish a criterion for automorphisms of finite-dimensional algebras. As an application, we will describe all automorphisms of the single-parameter generalized quaternion algebra. Additionally, we will obtain all automorphisms of Sweedler's 4-dimensional Hopf algebra.

Keywords

Hopf algebramatrixautomorphismquaternion

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Electronic Research Archive
Volume 32 Issue 11,
November 2024
Pages 6140-6152
DOI: 10.3934/era.2024285

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Yang Y, Chen Q. The criteria for automorphisms on finite-dimensional algebras. Electronic Research Archive, 2024, 32(11): 6140-6152. https://doi.org/10.3934/era.2024285

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Received: 06 September 2024
Revised: 05 November 2024
Accepted: 07 November 2024
Published: 15 November 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)