Deformations and extensions of modified $\lambda$-differential Lie-Yamaguti algebras

In this paper, we first introduce the concept and representations of modified $\lambda$-differential Lie-Yamaguti algebras. We then establish the cohomology of a modified $\lambda$-differential Lie-Yamaguti algebra with coefficients in a representation. As applications, we investigate the formal deformations and abelian extensions of modified $\lambda$-differential Lie-Yamaguti algebras by using the second cohomology group.