Solenoids in automorphism groups of evolution algebras
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 ofA 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.