On equivariant Lie-Yamaguti algebras and related structures
Shuangjian Guo, Bibhash Mondal, Ripan Saha
TL;DR
This paper develops a cohomology and deformation theory for Lie-Yamaguti algebras, especially under finite group actions, establishing an equivariant cohomology framework that captures deformation properties.
Contribution
It introduces equivariant cohomology for Lie-Yamaguti algebras with group actions and links it to deformation theory, extending existing algebraic deformation concepts.
Findings
Defined equivariant cohomology for Lie-Yamaguti algebras
Established the connection between equivariant cohomology and deformation theory
Showed that the developed cohomology is suitable for studying equivariant deformations
Abstract
In this paper, we first discuss cohomology and a one-parameter formal deformation theory of Lie-Yamaguti algebras. Next, we study finite group actions on Lie-Yamaguti algebras and introduce equivariant cohomology for Lie-Yamaguti algebras equipped with group actions. Finally, we study an equivariant one-parameter formal deformation theory and show that our equivariant cohomology is the suitable deformation cohomology.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology