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arXiv · 2507.20743

Virtually abelian symmetry groups of hyperbolic lattices

Simon Brandhorst·Markus Kirschmer·Giacomo Mezzedimi
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Abstract

We give a classification of integral lattices with virtually abelian symmetry group. As a consequence, we complete the classification of K3 surfaces with virtually abelian automorphism group. In the appendix we formulate an algorithm for weak approximation in orthogonal groups and use it to determine if two indefinite lattices are isometric.

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Simon Brandhorst, Markus Kirschmer, Giacomo Mezzedimi. 2025-07-28. Virtually abelian symmetry groups of hyperbolic lattices. https://arxiv.org/abs/2507.20743

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