Journal of Lie Theory 21 (2011), No. 4, 813--836
Copyright Heldermann Verlag 2011
Cohomology and Deformations of Hom-algebras
Faouzi Ammar
Université de Sfax, Faculté des Sciences, B. P. 1171, 3000 Sfax, Tunisia
Faouzi.Ammar@rnn.fss.tn
Zeyneb Ejbehi
Université de Sfax, Faculté des Sciences, B. P. 1171, 3000 Sfax, Tunisia
ejbehizeyneb@yahoo.fr
Abdenacer Makhlouf
Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et Applications, 4 Rue des Frères Lumière, 68093 Mulhouse, France
Abdenacer.Makhlouf@uha.fr
The purpose of this paper is to define cohomology structures on Hom-associative algebras and Hom-Lie algebras. The first and second coboundary maps were introduced by Makhlouf and Silvestrov in the study of one-parameter formal deformations theory. Among the relevant formulas for a generalization of Hochschild cohomology for Hom-associative algebras and a Chevalley-Eilenberg cohomology for Hom-Lie algebras, we define a Gerstenhaber bracket on the space of multilinear mappings of Hom-associative algebras and a Nijenhuis-Richardson bracket on the space of multilinear maps of Hom-Lie algebras. Also we enhance the deformation theory of this Hom-algebras by studying the obstructions.
Keywords: Hom-Lie algebra, cohomology, deformation.
MSC: 16S80,16E40,17B37,17B68
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