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- W4288366959 abstract "In the theory of unitary group representations, a group is called type I if all factor representations are of type I, and by a celebrated theorem of James Glimm [Gli61b], the type I groups are precisely those groups for which the irreducible unitary representations are what descriptive set theorists now call concretely classifiable. Elmar Thoma [Tho64] proved the following surprising characterization of the countable discrete groups of type I: They are precisely those that contain a finite index abelian subgroup. In this paper we give a new, simpler proof of Thoma's theorem, which relies only on relatively elementary methods. [Gli61b] James Glimm, Type I $C^{ast} $-algebras, Ann. of Math. (2) 73 (1961), 572--612. MR 0124756 [Tho64] Elmar Thoma, Uber unitare Darstellungen abzahlbarer, diskreter Gruppen, Math. Ann. 153 (1964), 111--138. MR 0160118" @default.
- W4288366959 created "2022-07-29" @default.
- W4288366959 creator A5012889206 @default.
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- W4288366959 date "2019-04-16" @default.
- W4288366959 modified "2023-09-26" @default.
- W4288366959 title "A short proof of Thoma's theorem on type I groups" @default.
- W4288366959 doi "https://doi.org/10.48550/arxiv.1904.08313" @default.
- W4288366959 hasPublicationYear "2019" @default.
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