Super Biderivation And Poisson Structure Of Twisted N=1 Schr?dinger-Neveu-Virasoro Algebra

Just like Killing form,a profound definition is of great benefit to the understanding of Lie algebra theory.Derivation is also an important concept in Lie algebra and plays an important role in the structure theory of Lie algebra.Biderivation is a generalization of the derivation.By calculating biderivation,we have the close relation between biderivation and commutative mapping,Post-Lie algebra.Similarly,if we extend the concept of biderivations to Lie superalgebras,we have the concept of super biderivations,which is the natural idea in Lie theory.Therefore,this paper studies the super biderivation structure of twisted N=1 Schr?dinger-Neveu-Schwarz algebras and the Poisson structure of twisted Schr?dinger-Virasoro algebras.Specifically,in the second chapter,this paper summarizes some basic properties from the biderivation of Lie algebras and application in commutative mappings and Post-Lie algebras.At the same time,the concept of super biderivations is obtained through generalization,and the super biderivations structure of twisted N=1 Schr?dinger-Neveu-Schwarz algebra is studied through lengthy calculation,we discuss the structure of super biderivations of twisted N=1 Schr?dinger-Neveu-Schwarz algebras and obtain the conclusion that all super biderivations of twisted N=1 Schr?dinger-Neveu-Schwarz algebras are inner super biderivations.In the third chapter,on the basis of the research on Poisson structure of Lie algebras W(0)by related authors,the Poisson structure of twisted N=1Schr?dinger-Neveu-Schwarz algebras is calculated,and obtain the Poisson structure of twisted Schr?dinger-Virasoro algebras is always trivial.