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Journal of Lie Theory 27 (2017), No. 1, 085--110
Copyright Heldermann Verlag 2017

Lattices of Oscillator Groups

Mathias Fischer
Institut für Mathematik und Informatik, E.-M.-Arndt-Universität, Walther-Rathenau-Strasse 47, 17487 Greifswald, Germany

This paper is concerned with discrete, uniform subgroups (lattices) of oscillator groups, which are certain semidirect products of the Heisenberg group and the additive group R of real numbers. The present paper classifies the lattices of the oscillator group up to automorphisms of the ambient Lie group. Moreover, by introducing discrete oscillator groups we can classify the abstract isomorphism type of lattices of some oscillator groups.

Keywords: Lattice, oscillator group.

MSC: 22E25, 22E40

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