Regular evolution algebras are universally finite

Abstract

In this paper we show that evolution algebras over any given field k \Bbbk are universally finite. In other words, given any finite group G G , there exist infinitely many regular evolution algebras X X such that A u t ( X ) ≅ G Aut(X)\cong 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. Finally, we show that any constant finite algebraic affine group scheme G \mathbf {G} over k \Bbbk is isomorphic to the algebraic affine group scheme of automorphisms of a regular evolution algebra.