COHOMOLOGY AND DEFORMATIONS OF HOM-LIE-YAMAGUTI COLOR ALGEBRAS

Hom-Lie-Yamaguti color algebras are defined and their representation and cohomology theory is considered. The (2, 3)-cocycles of a given Hom-Lie-Yamaguti color algebra T are shown to be very useful in a study of its deformations. In particular, it is shown that any (2, 3)-cocycle of T gives rise to a Hom-LieYamaguti color structure on T circle plus V, where V is a T-module, and that a one-parameter infinitesimal deformation of T is equivalent to that a (2; 3)-cocycle of T (with coefficients in the adjoint representation) defines a Hom-Lie-Yamaguti color algebra of deformation type.