Derivatives, Central Extensions, And Automorphisms Of GSW Lie Superalgebras

The GSW superalgebra Bε is a class of infinite dimensional complex Lie superalgebras introduced by Green,Schwarz and Witten in their study of superstring theory.In this thesis,we compute the first cohomology with coefficients in the adjoint module and classify all derivations of Bε;We determine the second cohomology with coefficients in the trivial module and obtain the universal central extension of the Ramond type GSW superalgebra B0.Finally,we classify all automorphisms and determine the structure of automorphism group of Bε.Our main result can be stated as follows:(1)The first cohomology of Bε with coefficients in the adjoint module H1(Bε,Bε)is three dimensional;(2)The second cohomology with coefficients in the trivial module for the Ramond type GSW superalgebra H2(B0,C)is three dimensional;(3)Tthe structure of automorphism group of Bε is given as follows:(?).