On Hom-Lie antialgebra |
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| Authors: | Tao Zhang Heyu Zhang |
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| Institution: | 1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, PR Chinazhangtao@htu.edu.cn;3. College of Mathematics and Information Science, Henan Normal University, Xinxiang, PR China |
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| Abstract: | AbstractIn this paper, we introduced the notion of Hom-Lie antialgebras. The representations and cohomology theory of Hom-Lie antialgebras are investigated. We prove that the equivalent classes of abelian extensions of Hom-Lie antialgebras are in one-to-one correspondence to elements of the second cohomology group. We also prove that 1-parameter infinitesimal deformation of a Hom-Lie antialgebra are characterized by 2-cocycles of this Hom-Lie antialgebra with adjoint representation in itself. The notion of Nijenhuis operators of Hom-Lie antialgebra is introduced to describe trivial deformations.Communicated by Dr. Pavel Kolesnikov |
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| Keywords: | Abelian extensions cohomology deformations Hom-Lie antialgebra Nijenhuis operators |
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