On symmetries of hyperbolic lattices of large rank

Torben Grabbel; Gebhard Martin; Giacomo Mezzedimi; Maia Raitz von Frentz; Paul Jakob Schmidt

doi:10.48550/arxiv.2602.05652

On symmetries of hyperbolic lattices of large rank

arXiv (Cornell University) 2026 Preprint Open access

Read full text

Authors: Torben Grabbel, Gebhard Martin, Giacomo Mezzedimi, Maia Raitz von Frentz, Paul Jakob Schmidt

DOI: 10.48550/arxiv.2602.05652

Cited by: 0

Abstract

For an even, integral hyperbolic lattice $L$, the symmetry group of $L$ is the quotient of the group of isometries of $L$ by the Weyl subgroup of $(-2)$-reflections. Following Nikulin, the exceptional lattice of $L$ is defined as the sublattice generated by elements that have finite orbit under the symmetry group of $L$. 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.

Fields of Study & Subjects

Algebraic Geometry and Number Theory Advanced Algebra and Geometry Geometric and Algebraic Topology

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 5 February 2026
Language: EN
Document type: Preprint