Group Representations, Volume 5Providing coverage of the theory of G-algebras (including Puis's theory) and block theory, this volume is divided into two parts: the first part sets out the foundations of the theory of G-algebras; while the second section is devoted to block theory, with a detailed proof of theorems. |
Contents
GAlgebras and Puigs Theory | 1 |
Interior GAlgebras | 111 |
Part A | 181 |
Copyright | |
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Apply Lemma Assume b₁ bG is defined bijection block idempotent block of RG BrRG central character central idempotent CG(P CG(x character of G classes of G commutative ring complete noetherian semilocal component conditions are equivalent conjugacy classes Corollary corresponding defect group defect pointed group desired conclusion follows direct embedding direct summand elements of G EndR(V exists finite group following result follows from Lemma G and let g E G G)-module group algebra height zero Hence homomorphism of R-algebras IBr(B ideal idempotent of RG induced integer interior G-algebra Irr(B Irr(G isomorphism Lemma Let H Math Moreover NG(P noetherian noetherian semilocal ring normal subgroup p-element p-group P,bp prime number primitive idempotent principal block Proof Proposition R-linear record the following representations result follows RG with defect semiperfect ring splitting field subgroup of G Sylow p-subgroup vertex write Z(FG Z(RG