Cohomology and deformations of crossed homomorphisms between Lie-Yamaguti algebras

Abstract

In this paper, we introduce the notion of crossed homomorphisms between Lie-Yamaguti algebras and establish the cohomology theory of crossed homomorphisms via the Yamaguti cohomology. Consequently, we use this cohomology to characterize linear deformations of crossed homomorphisms between Lie-Yamaguti algebras. We show that if two linear or formal deformations of a crossed homomorphism are equivalent, then their infinitesimals are in the same cohomology class in the first cohomology group. Moreover, we show that an order n deformation of a crossed homomorphism can be extended to an order n + 1 deformation if and only if the obstruction class in the second cohomology group is trivial.

3-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on 3-Lie algebras

“…Let (g, [•, •], •, •, • ) be a Lie-Yamaguti algebra. Recall in [46] that the center of g is denoted by…”