$\alpha$-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.j180850
Published 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
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