Only Countably Many Simply-Connected Lie Groups Admit Lattices.

Jörg Winkelmann

We prove that only countably many simply-connected real or complex Lie groups admit lattices. This result is essentially based on arithmeticity results of Mostow. In order to reduce the complex case to the real case we prove that a simply-connected real Lie group admits only finitely many complex structures compatible with the Lie group structure.