Journal of Lie Theory

no. 4
Cohomology and Deformations of Hom-algebras
Faouzi Ammar1; Zeyneb Ejbehi1; Abdenacer Makhlouf2
1Université de Sfax, Faculté des Sciences, B. P. 1171, 3000 Sfax, Tunisia
2Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et Applications, 4 Rue des Frères Lumière, 68093 Mulhouse, France
Journal of Lie Theory, Volume 21 (2011) no. 4, pp. 813-836
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.
DOI: 10.5802/jolt.650
Classification: 16S80,16E40,17B37,17B68
Keywords: Hom-Lie algebra, cohomology, deformation

Faouzi Ammar  1 ; Zeyneb Ejbehi  1 ; Abdenacer Makhlouf  2

1 Université de Sfax, Faculté des Sciences, B. P. 1171, 3000 Sfax, Tunisia
2 Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et Applications, 4 Rue des Frères Lumière, 68093 Mulhouse, France 
Faouzi Ammar; Zeyneb Ejbehi; Abdenacer Makhlouf. Cohomology and Deformations of Hom-algebras. Journal of Lie Theory, Volume 21 (2011) no. 4, pp. 813-836. doi: 10.5802/jolt.650
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     title = {Cohomology and {Deformations} of {Hom-algebras}},
     journal = {Journal of Lie Theory},
     pages = {813--836},
     year = {2011},
     volume = {21},
     number = {4},
     doi = {10.5802/jolt.650},
     zbl = {1237.17003},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.650/}
}
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