Some Results Of Supersymmetric Vertex Algebra And Supersymmetric Lie Conformal Algebra

Supersymmetric vertex algebra is a generalization of vertex algebra.We study the commutativity and nilpotency of supersymmetric vertex algebra and supersym-metric Lie conformal algebra,and the relationship between single supersymmetric vertex algebra and its associated supersymmetric Lie conformal algebra.Next we study the representation of the supersymmetric vertex algebra.We prove that the representation satisfies the weak associativity.Moreover,we establish the connection between field algebra on supersymmetric space and supersymmetric vertex algebra.Finally,we give the related results of generalized derivations of supersymmetric Lie conformal algebra.