Deformations and extensions of Lie–Yamaguti algebras.

The deformation and extension theory of Lie–Yamaguti algebras is studied. We prove that a 1-parameter infinitesimal deformation of a Lie–Yamaguti algebracorresponds to a Lie–Yamaguti algebra of deformation type and a (2,3)-cocycle ofwith coefficients in the adjoint representation. The notion of Nijenhuis operators for Lie–Yamaguti algebra is introduced to describe trivial deformations. We also prove that equivalence classes of abelian extensions of Lie–Yamaguti algebras are in one-to-one correspondence to elements of the (2,3)-cohomology group. [ABSTRACT FROM PUBLISHER]