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$\alpha$-type Hochschild cohomology of Hom-associative algebras and bialgebras
Benedikt Hurle,Abdenacer Makhlouf 대한수학회 2019 대한수학회지 Vol.56 No.6
In this paper we define a new type of cohomology for multiplicative Hom-associative algebras, which generalizes Hom-type Hochschild cohomology and fits with deformations of Hom-associative algebras including the deformation of the structure map $\alpha$. Moreover, we provide various observations and similarly a new type cohomology of Hom-bialgebras extending the Gerstenhaber-Schack cohomology for Hom-bialgebras and fitting with formal deformations including deformations of the structure map.
α-TYPE HOCHSCHILD COHOMOLOGY OF HOM-ASSOCIATIVE ALGEBRAS AND BIALGEBRAS
Hurle, Benedikt,Makhlouf, Abdenacer Korean Mathematical Society 2019 대한수학회지 Vol.56 No.6
In this paper we define a new type of cohomology for multiplicative Hom-associative algebras, which generalizes Hom-type Hochschild cohomology and fits with deformations of Hom-associative algebras including the deformation of the structure map ${\alpha}$. Moreover, we provide various observations and similarly a new type cohomology of Hom-bialgebras extending the Gerstenhaber-Schack cohomology for Hom-bialgebras and fitting with formal deformations including deformations of the structure map.