Reflection groups and Coxeter groups / James E. Humphreys

Auteur: Humphreys, James Edward (1939-) - AuteurType de document: MonographieCollection: Cambridge studies in advanced mathematics ; 29Langue: anglaisPays: Grande BretagneÉditeur: Cambridge : Cambridge University Press, 1997Edition: edition with correctionsDescription: 1 vol. (XII-204 p.) ; 23 cm ISBN: 0521436133 ; br. Note: This is a useful book. The style is informal and the arguments are clear. The publisher describes it as a "graduate textbook'' accessible to a reader with "a good knowledge of algebra'' which "attempts to be both an introduction to Bourbaki and an updating of the coverage''. This is fair billing. In its 200 pages it gives a readable introduction to Coxeter groups. It is the unique graduate level text on this subject and most of what it does is important for various aspects of Lie theory. The author keeps prerequisites to a minimum: the Euler characteristic of the Coxeter complex is computed without any topology and the section on invariants is written without any technicalities from commutative algebra or character theory. Occasional remarks hint at deeper connections with Lie theory. ... (MathSciNet)Bibliographie: Bibliogr. p. 185-202. Index. Sujets MSC: 20F55 Group theory and generalizations -- Special aspects of infinite or finite groups -- Reflection and Coxeter groups
20G05 Group theory and generalizations -- Linear algebraic groups and related topics -- Representation theory
51F15 Geometry -- Metric geometry -- Reflection groups, reflection geometries
20H15 Group theory and generalizations -- Other groups of matrices -- Other geometric groups, including crystallographic groups
En-ligne: Zentralblatt | MathSciNet
Location Call Number Status Date Due
Salle R 03534-01 / 20 HUM (Browse Shelf) Available

This is a useful book. The style is informal and the arguments are clear. The publisher describes it as a "graduate textbook'' accessible to a reader with "a good knowledge of algebra'' which "attempts to be both an introduction to Bourbaki and an updating of the coverage''. This is fair billing. In its 200 pages it gives a readable introduction to Coxeter groups. It is the unique graduate level text on this subject and most of what it does is important for various aspects of Lie theory. The author keeps prerequisites to a minimum: the Euler characteristic of the Coxeter complex is computed without any topology and the section on invariants is written without any technicalities from commutative algebra or character theory. Occasional remarks hint at deeper connections with Lie theory. ... (MathSciNet)

Bibliogr. p. 185-202. Index

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