On spectra of Koopman, groupoid and quasi-regular representations
| Autor: | Dudko, Artem, Grigorchuk, Rostislav |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | J. Mod. Dyn. 11 (2017), 99-123 |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we investigate relations between Koopman, groupoid and quasi-regular representations of countable groups. We show that for an ergodic measure class preserving action of a countable group G on a standard Borel space the associated groupoid and quasi-regular representations are weakly equivalent and weakly contained in the Koopman representation. Moreover, if the action is hyperfinite then the Koopman representation is weakly equivalent to the groupoid. As a corollary of our results we obtain a continuum of pairwise disjoint pairwise equivalent irreducible representations of weakly branch groups. As an illustration we calculate spectra of regular, Koopman and groupoid representations associated to the action of the 2-group of intermediate growth constructed by the second author in 1980. Comment: Some typos are fixed (including in Theorem 1 and in the proof of Kuhn's Theorem). Several passages not directly relevant to the proofs are removed. Other minor changes are performed |
| Databáze: | arXiv |
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