Structures Of Virasoro Conformal Superalgebra

In this thesis,we study the Lie conformal superalgebra associated to the Virasoro Lie superalgebra.It is called Virasoro conformal superalgebra,which is a free C（?）-module of rank 3 generated by{L,G,F}and satisfying Its Z₂-gradation is given by deg（L）=deg（F）=（?）,deg（G）=（?）.Firstly,we construct formal distributions with coefficients in the Virasoro Lie superalgebra,and then compute the corresponding λ-brackets,and thus obtain the Lie conformal superalgebra as required.Secondly,we study conformal derivations of the Virasoro conformal superalgebra and we prove that every conformal derivation dlis inner by discussing its parity.Thirdly,we compute 2-cocycles of the Virasoro conformal superalgebra with values in C.Then we show that the Virasoro conformal superalgebra has a unique universal three-dimensional central extension.Finally,we compute low-dimensional cohomologies of the Virasoro conformal superalgebra and we completely determine the 0th,first and second cohomology groups with trivial coefficients both for the basic and reduced complexes.