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Oct 7, 2018 at 16:16 history made wiki Post Made Community Wiki by Todd Trimble
Sep 8, 2018 at 1:10 comment added YCor Yes, the examples in the answer address the OP's question (4 out of 5 being about lattices in abelian groups, especially Euclidean lattices).
Sep 7, 2018 at 15:41 comment added Joe Silverman @YemonChoi But $\mathbb R^n$ is a locally compact Lie group, so geometry of numbers seems very relevant. For that matter, $(\mathbb Q_p^*)^n$ is a locally compact Lie group (although admittedly not a real Lie group), and its quotients by discrete subgroups are intimately connected to the theory of abelian varieties over $\mathbb Q_p$.
Sep 7, 2018 at 15:22 comment added Yemon Choi As do the tags chosen by the OP
Sep 7, 2018 at 15:16 comment added Yemon Choi Francesco, the body of the question makes it clear that the OP is only referring to lattices in (Lie) groups
Sep 7, 2018 at 13:13 history answered Francesco Polizzi CC BY-SA 4.0