2016/11/08 by Marco Bonatto, Bonatto, Marco, Dikran Dikranjan +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1611.02685
openalex publication_date 2016/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper compares two generalizations of Heisenberg groups and studies their connection to one of the major open problems in the field of locally compact abelian groups, namely the description of the self-dual locally compact abelian groups ([12]). The first generalization is presented by the so called generalized Heisenberg groups ℍ(ω), defined in analogy with the classical Heisenberg group and the second one is inspired by the construction proposed by Mumford in [16] and named after him as Weyl-Mumford groups (WM groups). These two families can be defined also in the framework of topological groups. We investigate the relationship between locally compact WM groups, locally compact Generalized Heisenberg with center isomorphic to \mathbbT and symplectic self-dualities.