2023/08/07 by Saikat Goswami, Goswami, Saikat · 1 citation
Mathematics · #17A30 #17A40 #17A42 #17D99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2308.03655
openalex publication_date 2023/08/07 · openalex created_date 2023/08/09 · openalex updated_date 2026/07/28
Infinitesimal deformation theory of Lie-Yamaguti algebras was introduced by Tao Zhang and Juan Li . We extend their theory to develop formal one-parameter deformation theory of Lie-Yamaguti algebras. It turns out that the right deformation cohomology which controls deformations in this context, is a variant of Lie-Yamaguti algebra cohomology which we introduce in this paper. At the end, we introduce the free object in the category of Lie-Yamaguti algebras and prove that it is rigid.