Abstract
We present an intrinsic characterization of the solvable Lie groups whose regular representation is a factor representation. The von Neumann algebras of these Lie groups turn out to be isomorphic to the hyperfinite factor of type II∞. The key to these results is the relation between square-integrable representations and the coadjoint action of solvable Lie groups.
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Acknowledgements
The research of the second-named author was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI—UEFISCDI, project number PN-III-P4-ID-PCE-2020-0878, within PNCDI III.
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Beltiţă, I., Beltiţă, D. (2023). Solvable Lie Groups with Factor Regular Representations. In: Kielanowski, P., Dobrogowska, A., Goldin, G.A., Goliński, T. (eds) Geometric Methods in Physics XXXIX. WGMP 2022. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-30284-8_13
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DOI: https://doi.org/10.1007/978-3-031-30284-8_13
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