Semisimple Algebras, Galois Actions, and Group Cohomology

Professor Robinson proposes to carry out a detailed study of the semisimplicity of crossed products. This topic falls within three important areas of algebra--group theory, ring theory, and cohomology of groups. The main problem to be studied involves the search for a 2-cocycle which will cause a given skew group algebra to be semisimple. This opens up some interesting problems about the structure of certain Galois modules, and about differentials in a spectral sequence. Progress has already been made. It is hoped that an intensive analysis of the various algebraic structures involved will contribute to a solution of the problem, and increase our understanding of the nature of semisimplicity.