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Additive Conjugacy and the Bohr Compactification of Orthogonal Representations

Chase, Zachary and Hann-Caruthers, Wade and Tamuz, Omer (2019) Additive Conjugacy and the Bohr Compactification of Orthogonal Representations. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200124-084913765

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Abstract

We say that two unitary or orthogonal representations of a finitely generated group G are additive conjugates if they are intertwined by an additive map, which need not be continuous. We associate to each representation of G a topological action that is a complete additive conjugacy invariant: the action of G by group automorphisms on the Bohr compactification of the underlying Hilbert space. Using this construction we show that the property of having almost invariant vectors is an additive conjugacy invariant. As an application we show that G is amenable if and only if there is a nonzero homomorphism from L²(G) into R/Z that is invariant to the G-action.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1905.11599arXivDiscussion Paper
ORCID:
AuthorORCID
Tamuz, Omer0000-0002-0111-0418
Record Number:CaltechAUTHORS:20200124-084913765
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200124-084913765
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100887
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 Jan 2020 20:00
Last Modified:24 Jan 2020 20:00

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