Derivations and Representations of Commutative Algebras Verifying a Polynomial Identity of Degree Five
Keywords:Generalized Almost-Jordan algebra, identity of degree five, Peirce decomposition, idempotent, derivation, representation
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.
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