Gerstenhaber-Schack Cohomology for Hom-bialgebras and Deformations
Khadra Dekkar, Abdenacer Makhlouf
TL;DR
This paper introduces a cohomology theory for Hom-bialgebras and explores their formal deformations, extending classical algebraic structures with twisted associativity conditions.
Contribution
It defines a Gerstenhaber-Schack cohomology complex specifically for Hom-bialgebras and investigates their deformation theory.
Findings
Established a cohomology framework for Hom-bialgebras
Analyzed formal deformation properties of Hom-bialgebras
Extended classical algebraic concepts to Hom-structures
Abstract
Hom-bialgebras and Hom-Hopf algebras are generalizations of bialgebra and Hopf algebra structures, where associativity and coassociativity conditions are twisted by a homomorphism. The purpose of this paper is to define a Gerstenhaber-Schack cohomology complex for Hom-bialgebras and then study one parameter formal deformations.
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