Deformation Cohomology of Lie-Yamaguti algebras and Free Lie-Yamaguti algebras
Saikat Goswami
TL;DR
This paper develops a formal deformation theory for Lie-Yamaguti algebras, introduces a new cohomology variant controlling these deformations, and proves the rigidity of free Lie-Yamaguti algebras.
Contribution
It extends existing deformation theory to formal one-parameter deformations and introduces a new cohomology variant specific to Lie-Yamaguti algebras.
Findings
Deformation cohomology is a variant of Lie-Yamaguti algebra cohomology.
The free Lie-Yamaguti algebra is proven to be rigid.
A formal deformation theory for Lie-Yamaguti algebras is established.
Abstract
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology