A Characterization of Associative Evolution Algebras

Evolution algebras are non-associative in general, that is, the binary multiplication law is not associative. However, there exist some of them that are associative. In this paper we deal with these last ones. We give an explicit classification of these algebras and show that the concept of associativity is equivalent to the existence of an unitary element for non-degenerate evolution algebras. We also explicitly describe the derivation space of these algebras.