Resumo

We introduce the concept of an associative representation for nonassociative algebras. Associative representations are constructed for Poisson, Malcev, and alternative algebras, with particular emphasis on the Cayley–Dickson algebra, which is represented by (8 \times 8) matrices. We then develop a general theory of associative representations and establish a criterion for their existence. This criterion is expressed in terms of the satisfaction of an identity involving an involution by the algebra under consideration.