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

  • BENEDIKT HURLE (a1) and ABDENACER MAKHLOUF (a1)

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.

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

  • BENEDIKT HURLE (a1) and ABDENACER MAKHLOUF (a1)

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