Structures Of Ramond N=2 Lie Conformal Superalgebra

In this thesis,we study a Lie conformal superalgebra of rank 4.It corresponds to the centereless Ramond N=2 Lie superalgebra?.We call it the Ramond N=2 Lie conformal superalgebra and denote it by C?.Firstly,we construct the?-valued formal distributions and then compute relations between them.Thus we can obtain the conformal set.Next we use the formal Fourier transform to define a?-bracket on the conformal set and thus we obtain the required Lie conformal superalgebra C?.Secondly,we calculate the conformal and generalized derivations of C?.According to the gradation of C?,we compute the derivations of C?in the odd and even cases,and we show that all the conformal derivations and generalized derivations of C?are inner.Thirdly,we study the central extension of the Ramond N=2 Lie conformal superalgebra.By calculating the 2-cocycle of C?,we obtain that it has a unique nontrivial universal central extension.Finally,we discuss the low-dimensional basic cohomologies and the reduced cohomologies of C?.It turns out that,for the trivial module?,the 0^th basic and reduced cohomology groups are one-dimensional,the 1^st and 2^nd basic cohomology groups together with the 1^st reduced cohomology group are trivial,whereas the 2ⁿdd reduced cohomology group is three dimensional.