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Continuity Criterion for Locally Bounded Endomorphisms of Connected Reductive Lie Groups

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Abstract

We prove that every locally bounded endomorphism \(\pi\) of a connected reductive Lie group taking the center of the group to the center is continuous if and only if the restriction \(\pi|_Z\) of \(\pi\) to the center \(Z\) of \(G\) is continuous with respect to the same topology.

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References

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Funding

Partially supported by SRISA according to the project FNEF-2022-0007 (Reg. no. 1021060909180-7-1.2.1).

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Authors and Affiliations

  1. Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991, Russia

    A. I. Shtern

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

    A. I. Shtern

  3. Scientific Research Institute for System Analysis of the Russian Academy of Sciences (FGU FNTs NIISI RAN), Moscow, 117312, Russia

    A. I. Shtern

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

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Shtern, A.I. Continuity Criterion for Locally Bounded Endomorphisms of Connected Reductive Lie Groups. Russ. J. Math. Phys. 30, 126–127 (2023). https://doi.org/10.1134/S1061920823010090

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  • DOI: https://doi.org/10.1134/S1061920823010090

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