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
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Methods of Representation Theory, Volume 2 Charles W. Curtis,Irving Reiner No preview available - 1994 |
Common terms and phrases
A(KG a₁ abelian algebra arbitrary assume B₁ block ideal block idempotent BN-pair Brauer commutative diagram commutative ring completes the proof conjugate Corollary corresponding Coxeter cyclic cyclic group D(ZG decomposition Dedekind domain defect group defined definition denote direct sum element exact sequence Exercise F₁ field finite group follows formula Frobenius functor G-set G₁ given GL(A Go(A group G group of order hence homomorphism idempotent indecomposable indecomposable modules induction integer irreducible characters K-algebra K₁(A kG-modules L₁ left A-modules Lemma Let G locally free M₁ matrix maximal ideal modules nonzero notation obtain p-adic p-block p-group P₁ parabolic subgroups permutation Picent prime Proposition prove R-order representation result RG-lattice S₁ semisimple simple simple modules subgroups of G subsection summand surjective Sylow p-subgroup T₁ Theorem unique V₁ vertex W₁ Weyl group X₁