Continuity criteria for locally bounded homomorphisms of certain Lie groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2023) no. 4, pp. 213-216.

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We prove that every locally bounded homomorphism of a connected Lie group $G$ whose commutator subgroup $G'$ admits a closed supplementary subgroup $Z$ such that $G=G'Z$ into a Lie group is continuous if and only if it is continuous on $Z$.
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A. I. Shtern. Continuity criteria for locally bounded homomorphisms of certain Lie groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 24 (2023) no. 4, pp. 213-216. http://geodesic.mathdoc.fr/item/FPM_2023_24_4_a11/

[1] Namioka I., “Separate continuity and joint continuity”, Pacific J. Math., 51 (1974), 515–531 | DOI | MR | Zbl

[2] Shtern A. I., “Continuity criteria for locally bounded endomorphisms of central extensions of perfect Lie groups”, Proc. Jangjeon Math. Soc., 26:2 (2023), 221–225 | MR | Zbl

[3] Shtern A. I., “Continuity criterion for locally bounded endomorphisms of connected reductive Lie groups”, Russ. J. Math. Phys., 30:1 (2023), 125–126 | DOI | MR

[4] Shtern A. I., “The discontinuity group of a locally bounded homomorphism of a connected Lie group into a connected Lie group is commutative”, Russ. J. Math. Phys., 30:3 (2023), 397–398 | DOI | MR | Zbl

[5] Shtern A. I., “Locally bounded automorphisms of connected Lie groups without nontrivial compact connected subgroups”, Adv. Stud. Contemp. Math., Kyungshang, 31:4 (2021), 501–504 | MR | Zbl

[6] Shtern A. I., “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 | MR | Zbl

[7] Shtern A. I., “Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture”, J. Math. Sci., 159:5 (2009), 653–751 | DOI | MR | Zbl

[8] Shtern A. I., “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 | DOI | MR | Zbl