Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras
Makhlouf, Abdenacer; Silvestrov, Sergei (2010). Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras. Forum Mathematicum, 22, (4), 715 - 739
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Published
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English
Authors:
Makhlouf, Abdenacer
;
Silvestrov, Sergei
Department:
Mathematics (Faculty of Engineering)
Non-commutative Geometry-lup-obsolete
Research Group:
Non-commutative Geometry-lup-obsolete
Abstract:
The aim of this paper is to extend to Hom-algebra structures the theory of 1-parameter formal deformations of algebras which was introduced by Gerstenhaber for associative algebras and extended to Lie algebras by Nijenhuis and Richardson. In this paper, formal deformations of Hom-associative and Hom-Lie algebras are studied. The first groups of a deformation cohomology are constructed and several examples of deformations are given. We also provide families of Hom-Lie algebras deforming Lie algebra sl(2)(K) and describe as formal deformations the q-deformed Witt algebra and Jackson sl(2)(K).
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