This article is cited in 6 papers

Topological groups with finite von Neumann algebras of type I

A. I. Shtern

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A complete description of all topological groups admitting a separating system of continuous irreducible finite-dimensional unitary representations of uniformly bounded dimensions is obtained. A similar description is obtained for the formally more general class of all unitarily representable topological groups whose von Neumann algebra is a sum of homogeneous summands of finite and uniformly bounded degrees. Related results are obtained; in particular, a description is given of all locally bounded topological groups all of whose irreducible unitary representations are finite-dimensional.

UDC: 512.546+517.987

MSC: Primary 22D12; Secondary 43A65, 47D03

Received: 28.02.2004

DOI: 10.4213/sm1279

 English version: Sbornik: Mathematics, 2005, 196:3, 447–463

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