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

2009/02/17 by Amira Ghorbel, Hatem Hamrouni
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Geometric and Algebraic Topology #math.GR #math.RA

paper · pdf · doi:10.3842/sigma.2009.020

published as SIGMA 5 (2009), 020, 17 pages

arxiv created 2009/02/17 · openalex publication_date 2009/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 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 Z r where r = dim(A).

Citations

• Discrete Cocompact subgroups of G₅3 and related C*-algebras