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α-TYPE CHEVALLEY–EILENBERG COHOMOLOGY OF HOM-LIE ALGEBRAS AND BIALGEBRAS
Published online by Cambridge University Press: 03 July 2019
Abstract
The purpose of this paper is to define an α-type cohomology, which we call α-type Chevalley–Eilenberg cohomology, for Hom-Lie algebras. We relate it to the known Chevalley–Eilenberg cohomology and provide explicit computations for some examples. Moreover, using this cohomology, we study formal deformations of Hom-Lie algebras, where the bracket as well as the structure map α are deformed. Furthermore, we provide a generalization of the grand crochet and study, in a particular case, the α-type cohomology for Hom-Lie bialgebras.
MSC classification
- Type
- Research Article
- Information
- Glasgow Mathematical Journal , Volume 62 , Special Issue S1: Workshop on Nonassociative algebras and their applications , December 2020 , pp. S108 - S127
- Copyright
- © Glasgow Mathematical Journal Trust 2019
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