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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.15604 |
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| _version_ | 1866912427188158464 |
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| author | Montoya, Mary Luz Rodiño Bedoya, Natalia A. Viana Henao, Carlos |
| author_facet | Montoya, Mary Luz Rodiño Bedoya, Natalia A. Viana Henao, Carlos |
| contents | Given an evolution algebra associated to a connected finite graph $Γ$, we exhibit a free action of the group of symmetries of $Γ$ on the set of automorphisms of the algebra. This allows us to explicitly describe this set and we prove that a sufficient condition for it to be finite is that every automorphism is induced by a graph symmetry. Consequently, we extend a known result about perfect evolution algebras to other families. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15604 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Group actions and automorphisms of evolution algebras associated to finite graphs Montoya, Mary Luz Rodiño Bedoya, Natalia A. Viana Henao, Carlos Rings and Algebras 17A36, 05E18 (Primary) 05C25, 05C81 (Secondary) Given an evolution algebra associated to a connected finite graph $Γ$, we exhibit a free action of the group of symmetries of $Γ$ on the set of automorphisms of the algebra. This allows us to explicitly describe this set and we prove that a sufficient condition for it to be finite is that every automorphism is induced by a graph symmetry. Consequently, we extend a known result about perfect evolution algebras to other families. |
| title | Group actions and automorphisms of evolution algebras associated to finite graphs |
| topic | Rings and Algebras 17A36, 05E18 (Primary) 05C25, 05C81 (Secondary) |
| url | https://arxiv.org/abs/2505.15604 |