Automorphism groups of Cayley evolution algebras

Abstract

In this paper we introduce a new species of evolution algebras that we call Cayley evolution algebras. We show that if a field $$\Bbbk $$ k contains sufficiently many elements (for example if $$\Bbbk $$ k is infinite) then every finite group G is isomorphic to $${\text {Aut}}(X)$$ Aut ( X ) where X is a finite-dimensional absolutely simple Cayley evolution $$\Bbbk $$ k -algebra.