Abstract reflections and Coxeter groups
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- by David M. Goldschmidt PDF
- Proc. Amer. Math. Soc. 67 (1977), 209-214 Request permission
Abstract:
A notion of “abstract reflection” is introduced and used to characterize the Coxeter groups. Several known results on Coxeter groups are obtained as easy corollaries.References
- N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238 H. S. M. Coxeter, The complete enumeration of finite groups of the form $R_i^2 = {({R_i}{R_j})^{{k_{ij}}}} = 1$, J. London Math. Soc. 10 (1935), 21-35.
- Jacques Tits, Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics, Vol. 386, Springer-Verlag, Berlin-New York, 1974. MR 0470099
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 67 (1977), 209-214
- MSC: Primary 20H15; Secondary 05C25
- DOI: https://doi.org/10.1090/S0002-9939-1977-0463328-2
- MathSciNet review: 0463328