Methods of Representation Theory, Volume 2Revised and expanded, this second volume presents a modern treatment of finite groups and orders. It covers classical, modular and integral representation theory and contains many important new results. Beginning with an introductory review of ring theory, algebraic number theory, and homological algebra, the book then moves on to other topics such as modular representations and integral representation theory. Also covered are class groups and Picard groups, the theory of blocks, rationality questions, indecomposable modules and more. |
Contents
Algebraic Ktheory | 1 |
39 Grothendieck groups of integral group rings | 44 |
40 Whitehead groups | 61 |
Copyright | |
43 other sections not shown
Other editions - View all
Methods of Representation Theory, Volume 2 Charles W. Curtis,Irving Reiner No preview available - 1994 |
Common terms and phrases
A-lattice A(KG a₁ abelian algebra arbitrary assume B₁ block ideal block idempotent BN-pair Brauer ch G character of G commutative diagram commutative ring completes the proof conjugate Corollary corresponding coset cyclic group D(ZG decomposition Dedekind domain defect group defined definition denote direct sum element exact sequence Exercise exists factor finite group follows formula G-set G₁ given group algebra group G group of order hence homomorphism idèle idempotent indecomposable indecomposable modules induction integer irreducible characters isomorphism classes K-algebra K₁(A left A-module Lemma Let G locally free M₁ matrix maximal ideal multiplication nonzero notation obtain p-adic p-block p-group P₁ parabolic subgroups permutation Picent prime projective Proposition prove R-order representation result RG-lattice root semisimple simple modules subgroups of G subsection summand surjective Sylow p-subgroup Theorem trivial unique vertex Weyl group