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Continuity Criterion for the Restriction to the Commutator Subgroup of a Locally Bounded Finite-Dimensional Representation of a Connected Lie Group

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Abstract

We prove that a locally bounded finite-dimensional representation of a connected Lie group has a continuous restriction with respect to the original topology of the group to the commutator subgroup of the group if and only if the restriction of the representation to the center of a Levi subgroup is continuous with respect to the original topology of the group.

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References

  1. A. I. Shtern, “Locally Bounded Finally Precontinuous Finite-Dimensional Quasirepresentations of Connected Locally Compact Groups,” Mat. Sb. 208 (10), 149–170 (2017); English transl., Sb. Math. 208 (10), 1557–1576 (2017).

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Acknowledgement

The research was partially supported by the Scientific Research Institute of System Analysis, Russian Academy of Sciences (FGU FNTs NIISI RAN), theme NIR 0065-2018-0004.

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Authors and Affiliations

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

    A. I. Shtern

  2. Scientific Research Institute for System Analysis of the Russian Academy of Sciences, 117312, Moscow, 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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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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Shtern, A.I. Continuity Criterion for the Restriction to the Commutator Subgroup of a Locally Bounded Finite-Dimensional Representation of a Connected Lie Group. Russ. J. Math. Phys. 26, 206–207 (2019). https://doi.org/10.1134/S1061920819020079

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  • DOI: https://doi.org/10.1134/S1061920819020079

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