Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
Makhlouf, Abdenacer; Silvestrov, Sergei (2007). Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras. Preprints in Mathematical Sciences
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Submitted
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English
Authors:
Makhlouf, Abdenacer
;
Silvestrov, Sergei
Department:
Mathematics (Faculty of Engineering)
Non-commutative Geometry-lup-obsolete
Project:
Non-commutative Analysis of Dynamics, Fractals and Wavelets
Non-commutative Geometry in Mathematics and Physics
Research Group:
Non-commutative Geometry-lup-obsolete
Abstract:
The aim of this paper is to extend to Hom-algebra structures the theory of formal deformations of algebras which was introduced by Gerstenhaber for associative algebras and extended to Lie algebras by Nijenhuis-Richardson. We deal with Hom-associative and Hom-Lie algebras. We construct the first groups of a deformation cohomology and give several examples of deformations. We provide families of Hom-Lie algebras deforming Lie algebra sl2 and describe as formal deformations the
q-deformed Witt algebra and Jackson sl2.
Keywords:
cohomology ;
Hom-Poisson algebra ;
Deformation ;
Hom-associative algebra ;
Hom-Lie algebra
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