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.
Key words and phrases: Lorentzian lattice, rootsystem, reflective lattice, reflexive lattice, cofinite reflection group, arithmetic reflection group.
1991 Mathematics Subject Classification: Primary 11E12; Secondary 20H15, 51F15.
Published in: J. of Number Theory 61 (1996), p. 103-144
Contact: Frank.Esselmann@Mathematik.Uni-Dortmund.DE