Moscow Mathematical Journal

Volume 15, Issue 3, July–September 2015 pp. 593–602.

Non-Arithmetic Hyperbolic Reflection Groups in Higher Dimensions

Authors: E. B. Vinberg
Author institution:Department of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 119991, Russian Federation

Summary:

We construct examples of non-arithmetic (non-cocompact) cofinite discrete reflection groups in n-dimensional Lobachevsky spaces Lⁿ for all n≤12 and for n=14, 18.

2010 Math. Subj. Class. 51F15, 22E40.

Keywords: Lobachevsky (hyperbolic) space, discrete group, reflection group, arithmetic group.

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