Central Extensions Of A Class Of Lie Superalgebras

In this paper,we study the one dimensional central extensions of a class of infinite dimensional Lie superalgebras,which can be obtained by 2|2 dimensional Balinsky-Novikov superalgebras affine construction.This paper is divided into four chapters:In the first chapter,we briefly introduce the research background and status and give the results on the(infinite dimensional)Lie superalgebras.In the second chapter,we introduce some basic definitions and conclusions used in this paper.In the third chapter,we introduce the central extensions of Lie superalgebras and bilinear forms on BN superalgebras.In the fourth chapter,we introduce the W(2,2)superalgebras and determine their 2-cocycle according to the bilinear form on 2|2-dimensional BN superalgebras which is corresponding to the Lie superalgebras.Fourthermore,we verify the 2-cocycle is a base of the 2-cohomology on W(2,2)superalgebras.