Isotopes of alternative algebras of characteristic different from

Abstract

Abstract We study homotopes of alternative algebras over an algebraically closed field of characteristic different from . We prove an analogue of Albert’s theorem on isotopes of associative algebras: in the class of finite-dimensional unital alternative algebras every isotopy is an isomorphism. We also prove that every -homotope of a unital alternative algebra preserves the identities of the original algebra. We also obtain results on the structure of isotopes of various simple algebras, in particular, Cayley–Dixon algebras.