Cohomology and deformations of compatible Hom-Lie algebras
Apurba Das
TL;DR
This paper develops a cohomology theory for compatible Hom-Lie algebras, characterizes them via Maurer-Cartan elements, and explores their extensions and deformations, extending previous Lie algebra work to a Hom-Lie setting.
Contribution
It introduces a new cohomology framework for compatible Hom-Lie algebras and applies it to study their extensions and deformations, generalizing existing theories.
Findings
Compatible Hom-Lie algebras characterized as Maurer-Cartan elements
Cohomology theory developed for these algebras
Applications to abelian extensions and deformation analysis
Abstract
In this paper, we consider compatible Hom-Lie algebras as a twisted version of compatible Lie algebras. Compatible Hom-Lie algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible Hom-Lie algebras generalizing the recent work of Liu, Sheng and Bai. As applications of cohomology, we study abelian extensions and deformations of compatible Hom-Lie algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Biological Activity of Diterpenoids and Biflavonoids · Algebraic structures and combinatorial models