1302.6291 (Run-Xuan Zhang)
Run-Xuan Zhang
The purpose of this paper is to develop a cohomology and deformation theories for generalized left-symmetric algebras.We introduce the notions of generalized left-symmetric cohomology and deformation. We also generalize a theorem of Dzhumadil'daev on connections between the right-symmetric cohomology and Chevalley-Eilenberg cohomology. As an application, we obtain a factorization theorem in left-symmetric superalgebras cohomology. Finally, we obtain all complex simple left-symmetric superalgebras of dimension 3 by the infinitesimal deformations of a given left-symmetric superalgebras.
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http://arxiv.org/abs/1302.6291
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