The criteria for automorphisms on finite-dimensional algebras
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.
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024285 |
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| author | Yanni Yang Quanguo Chen |
| author_facet | Yanni Yang Quanguo Chen |
| author_sort | Yanni Yang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f6471e96f2344e6ba4df3eeee597b21d |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-f6471e96f2344e6ba4df3eeee597b21d2025-01-23T07:53:00ZengAIMS PressElectronic Research Archive2688-15942024-11-0132116140615210.3934/era.2024285The criteria for automorphisms on finite-dimensional algebrasYanni Yang0Quanguo Chen1College of Mathematics and Statistics, Kashi University, Kashi 844000, ChinaCollege of Mathematics and Statistics, Kashi University, Kashi 844000, ChinaIn 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.https://www.aimspress.com/article/doi/10.3934/era.2024285hopf algebramatrixautomorphismquaternion |
| spellingShingle | Yanni Yang Quanguo Chen The criteria for automorphisms on finite-dimensional algebras Electronic Research Archive hopf algebra matrix automorphism quaternion |
| title | The criteria for automorphisms on finite-dimensional algebras |
| title_full | The criteria for automorphisms on finite-dimensional algebras |
| title_fullStr | The criteria for automorphisms on finite-dimensional algebras |
| title_full_unstemmed | The criteria for automorphisms on finite-dimensional algebras |
| title_short | The criteria for automorphisms on finite-dimensional algebras |
| title_sort | criteria for automorphisms on finite dimensional algebras |
| topic | hopf algebra matrix automorphism quaternion |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024285 |
| work_keys_str_mv | AT yanniyang thecriteriaforautomorphismsonfinitedimensionalalgebras AT quanguochen thecriteriaforautomorphismsonfinitedimensionalalgebras AT yanniyang criteriaforautomorphismsonfinitedimensionalalgebras AT quanguochen criteriaforautomorphismsonfinitedimensionalalgebras |