Regular evolution algebras are universally finite

Abstract

In this paper we show that evolution algebras over any given field k are universally finite. In other words, given any finite group G, there exist infinitely many regular evolution algebras X such that Aut(X) ∼ = G. The proof is built upon the construction of a covariant faithful functor from the category of finite simple (non oriented) graphs to the category of (finite dimensional) regular evolution algebras.