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Continuity Criteria for Locally Bounded Automorphisms of Central Extensions of Perfect Lie Groups

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Abstract

We prove that every locally bounded automorphism of a linear connected Lie central extension of a connected perfect Lie group is continuous if and only if it is continuous on the center. We also prove that, if \(Z\) is a connected Abelian group without nontrivial compact subgroups, \(H\) is a connected perfect Lie group and the short sequence of Lie groups \(\{e\}\to Z\to G\to H\to\{e\}\) is exact, then every locally bounded automorphism of \(G\) is continuous if and only if it is continuous on the center of \(G\).

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References

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Funding

Partially supported by the Moscow Center for Fundamental and Applied Mathematics.

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Correspondence to A. I. Shtern.

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Shtern, A.I. Continuity Criteria for Locally Bounded Automorphisms of Central Extensions of Perfect Lie Groups. Russ. J. Math. Phys. 28, 543–544 (2021). https://doi.org/10.1134/S1061920821040117

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  • DOI: https://doi.org/10.1134/S1061920821040117

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