Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups

Details Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups

2009-02-17

arxiv.org/abs/0902.2977v1

SIGMA 5 (2009), 020, 17 pages

Mathematics

Group Theory

Scientific paper

10.3842/SIGMA.2009.020

The discrete cocompact subgroups of the five-dimensional connected, simply
connected nilpotent Lie groups are determined up to isomorphism. Moreover, we
prove if $G=N\times A$ is a connected, simply connected, nilpotent Lie group
with an Abelian factor $A$, then every uniform subgroup of $G$ is the direct
product of a uniform subgroup of $N$ and ${\mathbb Z}^r$ where $r=\dim A$.

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