Skip to main content

Continuity Criterion for Locally Bounded Automorphisms of Central Extensions of Perfect Lie Groups with Discrete Center

Abstract

We prove that every locally bounded automorphism of a connected not necessarily linear Lie central extension of a connected perfect Lie group with discrete center is continuous if and only if it is continuous on the center.

This is a preview of subscription content, access via your institution.

References

  1. A. I. Shtern, “Locally Bounded Automorphisms of Connected Reductive Lie Groups”, Russ. J. Math. Phys., 28:3 (2021), 356–357.

    MathSciNet  Article  Google Scholar 

  2. A. I. Shtern, “A Version of van der Waerden’s Theorem and a Proof of Mishchenko’s Conjecture on Homomorphisms of Locally Compact Groups”, Izv. Math., 72:1 (2008), 169–205.

    MathSciNet  Article  Google Scholar 

  3. A. I. Shtern, “Finite-Dimensional Quasirepresentations of Connected Lie Groups and Mishchenko’s Conjecture”, J. Math. Sci. (N. Y.), 159:5 (2009), 653–751.

    MathSciNet  Article  Google Scholar 

  4. A. I. Shtern, “Locally Bounded Finally Precontinuous Finite-Dimensional Quasirepresentations of Locally Compact Groups”, Sb. Math., 208:10 (2017), 1557–1576.

    MathSciNet  Article  Google Scholar 

  5. A. I. Shtern, “A Criterion for the Continuity with Respect to the Original Group Topology of the Restriction to the Commutator Subgroup for a Locally Bounded Finite-Dimensional Representation of a Connected Lie Group”, Proc. Jangjeon Math. Soc., 22:1 (2019), 201–204.

    MathSciNet  MATH  Google Scholar 

  6. I. Namioka, “Separate Continuity and Joint Continuity”, Pacific J. Math., 51 (1974), 515–531.

    MathSciNet  Article  Google Scholar 

Download references

Funding

The research was partially supported by the Moscow Center for Fundamental and Applied Mathematics.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. I. Shtern.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shtern, A.I. Continuity Criterion for Locally Bounded Automorphisms of Central Extensions of Perfect Lie Groups with Discrete Center. Russ. J. Math. Phys. 29, 119–120 (2022). https://doi.org/10.1134/S1061920822010113

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061920822010113