(untitled) (European Journal of Pure and Applied Mathematics, 2023)
In this paper we study a class of commutative non associative algebras satisfying a polynomial identity of degree five. We show that under the assumption of the existence of a non-zero idempotent, any commutative algebra verifying such an identity admits a Peirce decomposition. Using this decomposition we proceeded to the study of the derivations and representations of algebras of this class.