FINITE-DIMENSIONAL ALGEBRAS OF INTEGRAL $ p$-ADIC REPRESENTATIONS OF FINITE GROUPS

Abstract

Let be a finite extension of the field of rational -adic numbers , the ring of integers of , a finite group, the ring of -representations of and ( is the ring of rational integers and the rational number field). We study the algebra in the case where the number of indecomposable -representations of is finite. In particular, for a -group and we find a list of the tensor products of indecomposable -representations of and obtain a description of the radical of and of the quotient algebra . It turns out that in this case we always have .Bibliography: 26 items.