Geodesic
Groups with Finite Dimensional Irreducible Multiplier Representations
Canadian journal of mathematics, Tome 37 (1985) no. 4, pp. 635-643

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a locally compact group and ω a normalized multiplier on G. Denote by V(G) (respectively by V(G, ω)) the von Neumann algebra generated by the regular representation (respectively co-regular representation) of G. Kaniuth [6] and Taylor [14] have characterized those G for which the maximal type I finite central projection in V(G) is non-zero (respectively the identity operator in V(G)).In this paper we determine necessary and sufficient conditions on G and ω such that the maximal type / finite central projection in V(G, ω) is non-zero (respectively the identity operator in V(G, ω)) and construct this projection explicitly as a convolution operator on L 2(G). As a consequence we prove the following statements are equivalent, (i) V(G, ω) is type I finite, (ii) all irreducible multiplier representations of G are finite dimensional, (iii) Gω (the central extension of G) is a Moore group, that is all its irreducible (ordinary) representations are finite dimensional. 
Holzherr, A. K. Groups with Finite Dimensional Irreducible Multiplier Representations. Canadian journal of mathematics, Tome 37 (1985) no. 4, pp. 635-643. doi: 10.4153/CJM-1985-033-2
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