Cohomology and Deformations of Crossed Homomorphisms Between Lie-Yamaguti Algebras

We introduce the notion of crossed homomorphisms between Lie-Yamaguti algebras and establish the cohomology theory of crossed homomorphisms via the Yamaguti cohomology. Accordingly, we use this cohomology to characterize linear deformations of crossed homomorphisms between Lie-Yamaguti algebras. If two linear or formal deformations of a crossed homomorphism are equivalent, then we show that their infinitesimals are in the same cohomology class. Moreover, we show that an order [Formula: see text] deformation of a crossed homomorphism can be extended to an order [Formula: see text] deformation if and only if the obstruction class is trivial.