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Connected Lie groups having faithful locally bounded (not necessarily continuous) finite-dimensional representations

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Abstract

In the paper, it is proved that a connected Lie group admits a (possibly discontinuous) faithful finite-dimensional representation if and only if it admits a continuous faithful finite-dimensional representation, i.e., if and only if it is a linear Lie group.

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Authors and Affiliations

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

    A. I. Shtern

  2. Institute of Systems Research (VNIISI), Russian Academy of Sciences, Moscow, 117312, Russia

    A. I. Shtern

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

Additional information

Partially supported by the Russian Foundation for Basic Research under grant no. 08-01-00034 and by the Program of Supporting Leading Scientific Schools under grant no. NSh-1562.2008.1.

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Shtern, A.I. Connected Lie groups having faithful locally bounded (not necessarily continuous) finite-dimensional representations. Russ. J. Math. Phys. 16, 566–567 (2009). https://doi.org/10.1134/S1061920809040116

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  • DOI: https://doi.org/10.1134/S1061920809040116

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