2015/01/13 by Tao Zhang, Juan Li · 22 citations
Mathematics · #Abelian group #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Equivalence (formal languages) #Homotopy and Cohomology in Algebraic Topology #Infinitesimal #Lie algebra #Lie conformal algebra #Mathematical analysis #Mathematics #Pure mathematics
paper · doi:10.1080/03081087.2014.1000815
published in Linear and Multilinear Algebra 63(11), 2212-2231 (Taylor & Francis)
openalex publication_date 2015/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.