Solenoids in automorphism groups of evolution algebras
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866918026967777280 |
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| author | Casado, Yolanda Cabrera Gonçalves, Maria Inez Cardoso Gonçalves, Daniel Barquero, Dolores Martín González, Cándido Martín Campos, Iván Ruiz |
| author_facet | Casado, Yolanda Cabrera Gonçalves, Maria Inez Cardoso Gonçalves, Daniel Barquero, Dolores Martín González, Cándido Martín Campos, Iván Ruiz |
| contents | Let A be an evolution algebra (possibly infinite-dimensional) equipped with a fixed natural basis B, and let E be the associated graph defined by Elduque and Labra. We describe the group of automorphisms of A that are diagonalizable with respect to B. This group arises as the inverse limit of a functor (a diagram) from the category associated with the graph E to the category of groups. In certain cases, this group can be realized as a dyadic solenoid. Additionally, we investigate the automorphisms that permute (and possibly scale) the elements of B. In particular, for algebras satisfying the 2LI condition, we provide a complete description of their automorphism group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14584 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solenoids in automorphism groups of evolution algebras Casado, Yolanda Cabrera Gonçalves, Maria Inez Cardoso Gonçalves, Daniel Barquero, Dolores Martín González, Cándido Martín Campos, Iván Ruiz Rings and Algebras Commutative Algebra Dynamical Systems 05C25, 08A35, 17A36, 17A60, 17D92 Let A be an evolution algebra (possibly infinite-dimensional) equipped with a fixed natural basis B, and let E be the associated graph defined by Elduque and Labra. We describe the group of automorphisms of A that are diagonalizable with respect to B. This group arises as the inverse limit of a functor (a diagram) from the category associated with the graph E to the category of groups. In certain cases, this group can be realized as a dyadic solenoid. Additionally, we investigate the automorphisms that permute (and possibly scale) the elements of B. In particular, for algebras satisfying the 2LI condition, we provide a complete description of their automorphism group. |
| title | Solenoids in automorphism groups of evolution algebras |
| topic | Rings and Algebras Commutative Algebra Dynamical Systems 05C25, 08A35, 17A36, 17A60, 17D92 |
| url | https://arxiv.org/abs/2505.14584 |