Group actions and automorphisms of evolution algebras associated to finite graphs

Abstract

Given an evolution algebra associated to a connected finite graph $\Gamma$, we exhibit a free action of the group of symmetries of $\Gamma$ 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.

19 pages, 7 figures