From the reviews of the French edition: "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or "Tits systems". A historical note provides a survey of the contexts in which groups generated by reflections have arisen. A brief introduction includes almost the only other mention of Lie groups and algebras to be found in the volume. Thus the presentation here is really quite independent of Lie theory. The choice of such an approach makes for an elegant, self-contained treatment of some highly interesting mathematics, which can be read with profit and with relative ease by a very wide circle of readers (and with delight by many, if the reviewer is at all representative)."(G.B. Seligman in MathReviews)
Includes bibliographical references (p. -257) and index.
Ch. IV. Coxeter Groups and Tits Systems: Coxeter Groups. Tits Systems.- Ch. V. Groups Generated by Reflections: Hyperplanes, Chambers and Facets. Reflections. Groups of Displacements Generated by Reflections. The Geometric Representation of a Coxeter Group. Invariants in the Symmetric Algebra. The Coxeter Transformation.- Ch. VI. Root Systems: Root Systems. Affine Weyl Group. Exponential Invariants. Classification of Root Systems.- Historical Note.
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