Evolution algebras that are almost Jordan

Abstract

In this paper, we give a necessary and sufficient condition for an almost Jordan algebra, which is also called Lie triple algebra to be an evolution algebra. We study the nilpotency, power associativity of such algebras. We specify the necessary and sufficient conditions for such an algebra to be baric. Along the way we show that train evolution algebras which are almost Jordan algebras are of rank at most 5. We prove that any finite-dimensional non-nil-evolution algebra verifying the identity of almost Jordan algebras has at least one non-zero idempotent. Finally, we study the derivations of this class of algebras.