A natural Morita equivalence reduction for some blocks of G-crossed product -lattices and applications to the Clifford theory of finite group modular representation theory

Abstract

Let be a complete discrete valuation ring with an algebraically closed residue field of characteristic p. Let G be a finite group and let A be a G-crossed product finitely generated -lattice.Section 1 presents a “natural Morita equivalence” reduction for some blocks of A. This setting was pioneered by E. C. Dade and extends some results of A. Hida and S. Koshitani, for example.In Section 2, we apply results in Section 1 and a basic result of Knorr to Finite Group Block Theory. In particular, we obtain a “lift from k to ” of fundamental results of Külshammer. This latter result has recently also been obtained by F. Eisele. We also present an “axiomitization” of the proof of an important result of B. Külshammer and some examples.