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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 5, Pages 1072–1112 (Mi izv2148)  

This article is cited in 36 scientific papers (total in 37 papers)

Discrete linear groups generated by reflections

È. B. Vinberg

Abstract: We investigate linear groups generated by reflections in the faces of a convex polyhedral cone and operating discretely on an open convex cone. These groups generalize the discrete groups of motions in simply connected spaces of constant curvature, generated by reflection. Like the latter, they turn out to be Coxeter groups.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:5, 1083–1119

Bibliographic databases:

UDC: 519.45
MSC: Primary 20H15, 50C15; Secondary 52F05, 52A25, 50C20
Received: 16.06.1970

Citation: È. B. Vinberg, “Discrete linear groups generated by reflections”, Izv. Akad. Nauk SSSR Ser. Mat., 35:5 (1971), 1072–1112; Math. USSR-Izv., 5:5 (1971), 1083–1119

Citation in format AMSBIB
\by \`E.~B.~Vinberg
\paper Discrete linear groups generated by reflections
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 5
\pages 1072--1112
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 5
\pages 1083--1119

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    This publication is cited in the following articles:
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    2. V.G Kac, “Infinite-dimensional algebras, Dedekind's η-function, classical möbius function and the very strange formula”, Advances in Mathematics, 30:2 (1978), 85  crossref
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    4. V. V. Nikulin, “On arithmetic groups generated by reflections in Lobachevskii spaces”, Math. USSR-Izv., 16:3 (1981), 573–601  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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    7. Victor G Kač, Dale H Peterson, “Infinite-dimensional Lie algebras, theta functions and modular forms”, Advances in Mathematics, 53:2 (1984), 125  crossref
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    16. M Salvetti, “Artin groups associated to infinite Coxeter groups”, Discrete Mathematics, 163:1-3 (1997), 129  crossref  elib
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    30. Daniel Allcock, “Reflection centralizers in Coxeter groups”, Transformation Groups, 2013  crossref
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    32. Gaifullin A., “Universal Realisators for Homology Classes”, Geom. Topol., 17:3 (2013), 1745–1772  crossref  isi
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