On deformation cohomology of compatible Hom-associative algebras
Taoufik Chtioui, Ripan Saha
TL;DR
This paper develops a cohomology theory for compatible Hom-associative algebras, viewing them as Maurer-Cartan elements in a graded Lie algebra, and explores their extensions and deformations.
Contribution
It introduces a generalized cohomology framework for compatible Hom-associative algebras and links them to Maurer-Cartan elements, expanding the understanding of their structure and deformations.
Findings
Characterization as Maurer-Cartan elements in a bidifferential graded Lie algebra
Definition of a new cohomology theory for compatible Hom-associative algebras
Analysis of abelian extensions and deformations using the cohomology
Abstract
In this paper, we consider compatible Hom-associative algebras as a twisted version of compatible associative algebras. Compatible Hom-associative algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible Hom-associative algebras generalizing the classical case. As applications of cohomology, we study abelian extensions and deformations of compatible Hom-associative algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons