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arXiv · 2505.14584

Solenoids in automorphism groups of evolution algebras

Yolanda Cabrera Casado·Maria Inez Cardoso Gonçalves·Daniel Gonçalves·Dolores Martín Barquero·Cándido Martín González·Iván Ruiz Campos
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Abstract

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.

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Yolanda Cabrera Casado, Maria Inez Cardoso Gonçalves, Daniel Gonçalves, Dolores Martín Barquero, Cándido Martín González, Iván Ruiz Campos. 2025-05-20. Solenoids in automorphism groups of evolution algebras. https://arxiv.org/abs/2505.14584

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