A Study On A Class Of Block-type Lie Superalgebras

From the mathematical point of view,Lie superalgebra is an algebraic branch developed on the basis of algebra.The research methods of Lie superalgebra are often studied by means of Lie algebra.In this paper,we study a class of Lie super-algebra of Block type by using the method of the algebra of Block type.In this paper,we systematically research the central expansion of a class of subalgebras of Lie superalgebra of Block type BS(q).Firstly,it introduces the background,purpose and significance of research status and development trend of this study as well;Then a class of Block type algebra BS(q)is obtained by BN superalgebrawe,which proves that it is a Lie superalgebra;Finally calculates the non-trivial expansion of a class of subalgebra of BS(q)and thus depicts its second-order cohomology group.