Abstract
We prove that every locally bounded automorphism of a reductive Lie group is continuous.
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References
V. S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations, Prentice-Hall Inc., Englewood Cliffs, NJ, 1974.
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.
A. I. Shtern, “Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko’s conjecture”, J. Math. Sci. (N. Y.), 159:5 (2009), 653–751.
A. I. Shtern, “Locally Bounded Finally Precontinuous Finite-Dimensional Quasirepresentations of Locally Compact Groups”, Sb. Math., 208:10 (2017), 1557–1576.
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.
I. Namioka, “Separate continuity and joint continuity”, Pacific J. Math., 51 (1974), 515–531.
Funding
Partially supported by the Moscow Center for Fundamental and Applied Mathematics.
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Shtern, A.I. Continuity Criterion for Locally Bounded Automorphisms of Connected Reductive Lie Groups. Russ. J. Math. Phys. 28, 356–357 (2021). https://doi.org/10.1134/S1061920821030080
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DOI: https://doi.org/10.1134/S1061920821030080