The criteria for automorphisms on finite-dimensional algebras

Yanni Yang; Quanguo Chen; Yanni Yang; Quanguo Chen

doi:10.3934/era.2024285

Electronic Research Archive

2024, Volume 32, Issue 11: 6140-6152. doi: 10.3934/era.2024285

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Research article

The criteria for automorphisms on finite-dimensional algebras

Yanni Yang ^1,2,
Quanguo Chen ^{1
,
,}

1.
College of Mathematics and Statistics, Kashi University, Kashi 844000, China
2.
School of Mathematical science, Nankai University, Tianjin 300071, China

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

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.
- Hopf algebra,
- matrix,
- automorphism,
- quaternion
Citation: Yanni Yang, Quanguo Chen. The criteria for automorphisms on finite-dimensional algebras[J]. Electronic Research Archive, 2024, 32(11): 6140-6152. doi: 10.3934/era.2024285

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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.

References

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