The Frobenius P-category of a block

Abstract

3.1 Let G be a finite group, k an algebraically closed field of characteristic p, b a primitive idempotent of the center Z(kG) of the group algebra kG — so that (b, G) is a block, or b is a block of G (cf. 1.10) — and (P, e) a maximal Brauer (b, G)-pair (cf. 1.15). In this chapter, we describe the Frobenius P-category F_(b,G) associated with (b, G); although strictly speaking it depends on the choice of (P, e), it will be immediately clear that the different choices determine equivalent categories and that this dependence is ultimately unessential.