Even unimodular Lorentzian lattices and hyperbolic volume

TL;DR

This paper calculates the hyperbolic volume of automorphism groups of even unimodular Lorentzian lattices, linking lattice theory with hyperbolic geometry and arithmetic orbifold volumes.

Contribution

It provides explicit hyperbolic covolume computations for automorphism groups of these special lattices, extending previous work on hyperbolic orbifold volumes.

Findings

Computed covolumes for all such lattices

Connected lattice automorphisms with hyperbolic orbifold volumes

Extended previous volume calculations using Prasad's formula

Abstract

We compute the hyperbolic covolume of the automorphism group of each even unimodular Lorentzian lattice. The result is obtained as a consequence of a previous work with Belolipetsky, which uses Prasad's volume to compute the volumes of the smallest hyperbolic arithmetic orbifolds.