Geodesic
Topological groups with finite von Neumann algebras of type~I
Sbornik. Mathematics, Tome 196 (2005) no. 3, pp. 447-463

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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. 
@article{SM_2005_196_3_a5,
     author = {A. I. Shtern},
     title = {Topological groups with finite von {Neumann} algebras of {type~I}},
     journal = {Sbornik. Mathematics},
     pages = {447--463},
     publisher = {mathdoc},
     volume = {196},
     number = {3},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_3_a5/}
}
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A. I. Shtern. Topological groups with finite von Neumann algebras of type~I. Sbornik. Mathematics, Tome 196 (2005) no. 3, pp. 447-463. http://geodesic.mathdoc.fr/item/SM_2005_196_3_a5/