  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.
