Uber die maximale Dimension von Lorentz-Gittern mit coendlicher Spiegelungsgruppe

Author: Esselmann F.

Source: Journal of Number Theory, Volume 61, Number 1, November 1996 , pp. 103-144(42)

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Abstract:

In [Vi4] Vinberg has given a lemma relating ℤ -lattices of signature ( n ,?1) having a cofinite reflection group with certain positive definite, reflective sublattices, i.e. sublattices having a root system of maximal rank. This paper contains a detailed investigation of the existence of non reflective positive definite lattices in high dimensional genera. As a consequence of these results and Vinberg's lemma, the maximal dimension of ℤ -lattices of signature ( n ,?1) with a cofinite reflection group is determined to be n +1=22.

Language: German

Document Type: Research article

Affiliations: Fachbereich Mathematik, Universitat Dortmund, Dortmund, D-44221, Germany

Publication date: 1996-11-01