  The goal of the present paper is to investigate non-abelian extensions of
Lie-Yamaguti algebras and explore extensibility of a pair of automorphisms
about a non-abelian extension of Lie-Yamaguti algebras. First, we study
non-abelian extensions of Lie-Yamaguti algebras and classify the non-abelian
extensions in terms of non-abelian cohomology groups. Next, we characterize the
non-abelian extensions in terms of Maurer-Cartan elements. Moreover, we discuss
the equivalent conditions of the extensibility of a pair of automorphisms about
a non-abelian extension of Lie-Yamaguti algebras, and derive the fundamental
sequences of Wells in the context of Lie-Yamaguti algebras. Finally, we discuss
the previous results in the case of abelian extensions of Lie-Yamaguti
algebras.
