On associative representations of non-associative algebras

摘要

We define a notion of associative representation for algebras. We prove the existence of faithful associative representations for any alternative, Mal'cev, and Poisson algebra, and prove analogs of Ado-Iwasawa theorem for each of these cases. We construct also an explicit associative representation of the Cayley-Dickson algebra in the matrix algebra M-8(F).