We explicitly compute the first and second cohomology groups of the Schrdinger algebra S(1) with coefficients in the trivial module and the finite-dimensional irreducible modules.We also show that the first and second cohomology groups of S(1) with coefficients in the universal enveloping algebras U(S(1))(under the adjoint action) are infinite dimensional.
In this paper, an explicit determinant formula is given for the Verma modules over the Lie algebra W(2, 2). We construct a natural realization of a certain vaccum module for the algebra W(2, 2) via the Weyl vertex algebra. We also describe several results including the irreducibility, characters and the descending filtrations of submodules for the Verma module over the algebra W(2, 2).
In this paper we study the homology and cohomology groups of the super Schrodinger algebra S(1/1)in(1+l)-dimensional spacetime.We explicitly compute the homology groups of S(1/1)with coefficients in the trivial module.Then using duality,we finally obtain the dimensions of the cohomology groups of S(1/1)with coefficients in the trivial module.
