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Almost Connected DMAP Groups Are FIR

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Abstract

Let DMAP be the class of locally compact groups that admit a (not necessarily continuous) embedding in a compact topological group, and let FIR be the class of locally compact groups all of whose continuous irreducible unitary representations are finite-dimensional. We prove that every almost connected DMAP group is an FIR group.

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Acknowledgement

Supported by the Scientific Research Institute for System Analysis of the Russian Academy of Sciences (the research corresponds to the theme no. 0065-2019-0007).

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    A. I. Shtern

  2. Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Moscow, 117312, Russia

    A. I. Shtern

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  1. A. I. Shtern
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Correspondence to A. I. Shtern.

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Shtern, A.I. Almost Connected DMAP Groups Are FIR. Russ. J. Math. Phys. 27, 137–138 (2020). https://doi.org/10.1134/S1061920820010136

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  • DOI: https://doi.org/10.1134/S1061920820010136

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