Classification Of Nilpotent Lie Superalgebras Of Multiplier-rank Less Than Or Equal To 2

Multiplier theory,as a branch of cohomology theory,the study of the math-ematics scholars in recent years is still very active.It has been applied in a wide range of insights.Therefore,the study of multiplier theory is of great significance.In this paper,we first give the concept of defining pair for Lie superalgebras.By studying the relation of multiplier(super-)dimention and upper bound of a multi-plier(super-)dimention,we introduce the concept of(super-)multiplier-rank for Lie superalgeras and classify all the finite-dimensional nilpotent Lie superalgebras of multiplier-rank?2 over an algebraically closed field of characteristic zero.In the process,we also determine the multipliers of Heisenberg superalgebras.