Journal of Lie Theory

no. 1
Lattices of Oscillator Groups
Journal of Lie Theory, Volume 27 (2017) no. 1, pp. 85-110
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.
DOI: 10.5802/jolt.934
Classification: 22E25, 22E40
Keywords: Lattice, oscillator group 
@article{JOLT_2017_27_1_a3,
     author = {M. Fischer},
     title = {Lattices of {Oscillator} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {85--110},
     year = {2017},
     volume = {27},
     number = {1},
     doi = {10.5802/jolt.934},
     zbl = {1362.22009},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.934/}
}
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M. Fischer. Lattices of Oscillator Groups. Journal of Lie Theory, Volume 27 (2017) no. 1, pp. 85-110. doi: 10.5802/jolt.934

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