2015/01/13 by Tao Zhang, Juan Li · 5 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.1080/03081087.2014.1000815
The deformation and extension theory of Lie–Yamaguti algebras is studied. We prove that a 1-parameter infinitesimal deformation of a Lie–Yamaguti algebra corresponds to a Lie–Yamaguti algebra of deformation type and a (2,3)-cocycle of with 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.