COHOMOLOGY THEORY AND DEFORMATIONS OF Z2-GRADED LIE-ALGEBRAS

The algebraic cohomology and the spectral sequences for a Z 2-graded Lie algebra are briefly reviewed. The reducibility property of a strongly semisimple Lie superalgebra is established. The role of second and third cohomologies in the deformation of a Lie superalgebra is discussed. Using spectral sequences, the second cohomology of the full BRS algebra is shown to be the ground field and the third cohomology being trivial implies that osp(1,2) is the only graded Lie algebra obtained by deformation of the full BRS algebra. A similar analysis yields the superconformal algebra as a deformation of the super Poincaré algebra. The superconformal algebra so derived contains so(4,1) as the even part, ruling out the existence of negative curvature of a de Sitter universe! © 1990 American Institute of Physics.