Classification of finite factor representations of the \((2m+1)\)-dimensional Heisenberg group over a countable field of finite characteristic
type: Item
instance of: scholarly article
title: Classification of finite factor representations of the \((2m+1)\)-dimensional Heisenberg group over a countable field of finite characteristic
zbMATH Open document ID: 1027.22012
DOI: 10.1023/A:1020162424581
author: K. Kokhas'
publication date: 2004-01-13T00:00:00Z
review text: The Heisenberg groups considered in this paper are defined over an infinite algebraic extension of \(\mathbb{F}_p\). Let \(F\) be such a field; then the dual group of the additive group is no longer a one-dimensional \(F\)-module. The author announces without proofs a number of results concerning the representation theory of these groups. First of all he constructs a family of factor representations and states that this list is complete. Further he describes the decomposition of the regular representation and states the corresponding Plancherel theorem. Finally, he describes the Grothendieck group of the group algebra \(L^1(H)\cap L^2(H)\).
Mathematics Subject Classification ID: 22E27
zbMATH DE Number: 1930668
zbMATH Keywords: Bratteli diagram
zbMATH Keywords: Heisenberg groups
zbMATH Keywords: representation theory
zbMATH Keywords: Grothendieck group
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
full work available at URL: a:1020162424581
OpenAlex ID: W212252136
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1930668