2013/02/26 by Run-Xuan Zhang, Zhang, Run-Xuan
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Rings and Algebras (math.RA) #math-ph #math.MP #math.RA
paper · pdf · doi:10.48550/arxiv.1302.6291
arxiv created 2013/02/26 · arxiv updated 2013/02/27
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.