The Low Dimensional Classification And Universal Central Extensions Of Lie Poisson Superalgebras

Lie Poisson superalgebras have been developed from Lie Poisson algebras andLie superalgebras, which have two structures. The aim of this paper is to studythe low dimensional classification and universal central extansions of Lie Poissonsuperalgebras. We first present all necessary definitions such as subalgebra, ideal,homomorphism, derivation superalgebras in Lie Poisson superalgebras. Then wegive the low dimensional classification, properties of the central extensions anduniversal central extensions of Lie Poisson superalgebras, by constructing univer-sal central extensions, we obtain that the existence of the universal covering ifand only if the Lie Poisson superalgebras are perfect. Last we work on lifting ofautomorphisms and derivations of Lie Poisson superalgebras.