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 $\alpha$-type Hochschild cohomology of Hom-associative algebras and bialgebras J. Korean Math. Soc. 2019 Vol. 56, No. 6, 1655-1687 https://doi.org/10.4134/JKMS.j180850Published online November 1, 2019 Benedikt Hurle, Abdenacer Makhlouf Universit\'e de Haute Alsace; Universit\'e de Haute Alsace Abstract : 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. Keywords : cohomology, Hom-associative algebra, deformation, Hom-bialgebra, $L_\infty$-structure MSC numbers : 16W55, 16S99, 16S80, 16T10 Downloads: Full-text PDF   Full-text HTML