Derivations Of A Kind Of Block-type Lie Superalgebras And Their Applications

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.The inseparable connections between Lie algebras and Lie superalgebras,together with their physical and mathematical sig-nificance,make the related researches become the most dynamic field in mathemat-ics.In this paper,we study a class of Lie superalgebra of Block type by using the method of the algebra of Block type.First,by using the study method of the Lie algebra of Block type derivations,the dipole superconductor and the odd superderivation of the Lie superalgebra are studied,and the structure of the superderivation of the Lie superalgebra is given.In this paper,we mainly studies the Block type Lie superalgebra SB(q)and its superderivation subalgebra.First,the research background,the current research status and development trend at home and abroad are introduced.Then,the struc-ture of the Lie superalgebra SB(q)superderivation is given.Second,we discuss the application of superderivation in Lie superalgebra SB(q).We derive the structure of super-biderivations by giving the structure of superderiva-tion of Lie superalgebra.