On class algebras

Abstract

Let FαG be a twisted group algebra. A subalgebra of F αG generated by all class sums of partition P of G is called a projective class algebra in FαG associated with partition P. In this paper we study various partitions of G determined by actions of certain operator groups on G and construct projective class algebras depending on the actions. With regard to projective class algebras, we investigate structures of associated skew group algebras and fixed group algebras.