On Symmetries of Hyperbolic Lattices of Large Rank

For an even, integral hyperbolic lattice , the symmetry group of is the quotient of the group of positive isometries of by the Weyl subgroup of ‐reflections. Following Nikulin, the exceptional lattice of is defined as the sublattice generated by elements that have finite orbit under the symmetry group of . We prove that every hyperbolic lattice of rank at least 46 has trivial exceptional lattice. In particular, every such lattice admits a symmetry of maximal Salem degree.