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The algebraic cohomology and the spectral sequences for a Z2-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!

The structure of the collective bands of 76,78,80,82Sr are studied within our deformed configuration mixing shell model based on Hartree-Fock states. The self-conjugate nucleus 76Sr is found to be most deformed in the mass A=80 region in agreement with experiment. The deformation is found to decrease for heavier isotopes. The calculated positive and negative parity bands agree quite well with experiment. The calculated B(E2) values are compared with the available experimental results. The agreement is quite satisfactory.

The structure of collective bands in 74,76Kr is studied within the framework of the deformed configuration mixing shell model based on Hartree-Fock states. The active single-particle orbits are 1p3/2, 0f5/2, 1p1/2 and 0g9/2 with 56Ni as the inert core. A modified Kuo interaction has been used for the above configuration space. The 74Kr nucleus is found to be the most deformed nucleus among the krypton isotopes which is in agreement with experiment. The deformation is found to decrease for the 76Kr isotope. The calculated positive- and negative-parity bands agree quite well with the experiment for both the nuclei. A number of excited bands is also predicted. We have also calculated B(E2) values and compared them with available experimental data. The structure of the strongly coupled band built on K = 4( + ) in 76Kr is also studied.