On hyperbolic lattices whose reduced automorphism group is virtually abelian

Abstract

We give a classification of even integral lattices with virtually abelian reduced automorphism 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.

arXiv comment16 pages, with an appendix by Simon Brandhorst and Markus Kirschmer; v2: title changed, minor changes to the text, some references added