Quantization And Poisson Structure Of A Class Of Super W-algebras

Poisson algebra is derived from the study of Poisson geometry,and it plays an important role in the study of quantum group.At the same time,the quan-tization of Lie(super)algebra is an essential way to construct quantum group.In this paper,we will obtain the Poisson structure on the super-W algebra by the way of undetermined coefficients.And based on the Lie superbialgebra structure of the super-W algebra and using the quantization method proposed by V.Drinfeid,we can construct the Drinfeld torsion elements,then we quantize the Hopf superalgebraic on the the associative algebra of formal power series with coefficients in universal envelope algebra of the super-W algebra.In the final part,we get a family of non-commutative and non-cocommutative Hopf superalgebras.It is an important way to study the structure of algebras by studying generalized derivation,centroids and quasicentroids,then the generalized derivation of ternary Jordan superalgebra will be studied in the end of this paper.