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α-TYPE CHEVALLEY–EILENBERG COHOMOLOGY OF HOM-LIE ALGEBRAS AND BIALGEBRAS

Part of: Lie algebras and Lie superalgebras General nonassociative rings

Published online by Cambridge University Press:  03 July 2019

BENEDIKT HURLE  and
ABDENACER MAKHLOUF
ABDENACER MAKHLOUF
Affiliation:
IRIMAS, Département de Mathématiques, Université de Haute Alsace, Mulhouse, France e-mail: benedikt.hurle@uha.fr, Abdenacer.Makhlouf@uha.fr
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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.

Keywords

Lie TheoryDeformation TheoryNon-associative algebra

MSC classification

Primary: 17B62: Lie bialgebras; Lie coalgebras 17B56: Cohomology of Lie (super)algebras 17A30: Algebras satisfying other identities
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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