Adelic Case
A lattice of fundamental importance for the theory of automorphic forms is given by the group G(K) of K-points of a semisimple (or reductive) linear algebraic group G defined over a global field K. This group diagonally embeds into the adelic algebraic group G(A), where A is the ring of adeles of K, and is a lattice there. Unlike arithmetic lattices, G(K) is not finitely generated.
Read more about this topic: Lattice (discrete Subgroup)
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