- The structure of all n-homogeneous C-algebras with a given compact Hausdorft space X as maximal ideal space is looked at from a cohomological standpoint. Such algebras are matrix algebra bundles over X, and by means of fibrewise tensor products, a group, B(X), analogous to the Brauer group of field theory, is constructed. A partial cohomological description of this group is given. Projective representations of finite groups are used to provide examples where B(X) is precisely computable and nontrivial. American Mathematical Society 1972.