Geodesic
α-TYPE CHEVALLEY–EILENBERG COHOMOLOGY OF HOM-LIE ALGEBRAS AND BIALGEBRAS
Glasgow mathematical journal, Tome 62 (2020), pp. S108-S127

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DOI

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.
DOI : 10.1017/S0017089519000296
Mots-clés : Lie Theory, Deformation Theory, Non-associative algebra 
MAKHLOUF, ABDENACER. α-TYPE CHEVALLEY–EILENBERG COHOMOLOGY OF HOM-LIE ALGEBRAS AND BIALGEBRAS. Glasgow mathematical journal, Tome 62 (2020), pp. S108-S127. doi: 10.1017/S0017089519000296
@article{10_1017_S0017089519000296,
     author = {MAKHLOUF, ABDENACER},
     title = {\ensuremath{\alpha}-TYPE {CHEVALLEY{\textendash}EILENBERG} {COHOMOLOGY} {OF} {HOM-LIE} {ALGEBRAS} {AND} {BIALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {S108--S127},
     year = {2020},
     volume = {62},
     number = {S1},
     doi = {10.1017/S0017089519000296},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089519000296/}
}
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