International Centre for Theoretical Physics Cohomology Theory and Deformations of Z^graded Lie Algebras International Atomic Energy Agency United Nations Educational, Scientific and Cultural Organization

The algebraic cohoroology and the spectral sequences for a Z2-graded Lie algebra are briefly reviewed. The reducibility property of a strongly semisiiaple 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 full BRS algebra is shown to be W and the third cohomology being trivial implying that osp(l,2) is the only graded Lie algebra obtained by deformation of the full BRS algebra. MIRAMARE TRIESTE September 1988 * To be submitted for publication. >'<* Permanent address: Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.