Automatic continuity of a locally bounded homomorphism of Lie groups on the commutator subgroup
Sbornik. Mathematics, Tome 215 (2024) no. 6, pp. 861-868 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $G$ and $H$ be Lie groups, let $\pi\colon G\to H$ be a locally bounded homomorphism, and let $G'$ be the commutator subgroup of $G$. Then the restriction $\pi|_{G'}$ of the homomorphism $\pi$ to $G'$ is continuous. Bibliography: 8 titles.
Keywords: locally bounded homomorphism, discontinuity group of a homomorphism, commutator subgroup.
Mots-clés : Lie group homomorphism
@article{SM_2024_215_6_a7,
     author = {A. I. Shtern},
     title = {Automatic continuity of a~locally bounded homomorphism of {Lie} groups on the commutator subgroup},
     journal = {Sbornik. Mathematics},
     pages = {861--868},
     year = {2024},
     volume = {215},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2024_215_6_a7/}
}
TY  - JOUR
AU  - A. I. Shtern
TI  - Automatic continuity of a locally bounded homomorphism of Lie groups on the commutator subgroup
JO  - Sbornik. Mathematics
PY  - 2024
SP  - 861
EP  - 868
VL  - 215
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/SM_2024_215_6_a7/
LA  - en
ID  - SM_2024_215_6_a7
ER  - 
%0 Journal Article
%A A. I. Shtern
%T Automatic continuity of a locally bounded homomorphism of Lie groups on the commutator subgroup
%J Sbornik. Mathematics
%D 2024
%P 861-868
%V 215
%N 6
%U http://geodesic.mathdoc.fr/item/SM_2024_215_6_a7/
%G en
%F SM_2024_215_6_a7
A. I. Shtern. Automatic continuity of a locally bounded homomorphism of Lie groups on the commutator subgroup. Sbornik. Mathematics, Tome 215 (2024) no. 6, pp. 861-868. http://geodesic.mathdoc.fr/item/SM_2024_215_6_a7/

[1] A. I. Shtern, “Corrected automatic continuity conditions for finite-dimensional representations of connected Lie groups”, Russ. J. Math. Phys., 21:1 (2014), 133–134 | DOI | MR | Zbl

[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 | DOI

[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 | DOI

[4] R. Engelking, General topology, Monogr. Mat., 60, PWN–Polish Sci. Publ., Warsaw, 1977, 626 pp. | MR | Zbl

[5] A. I. Shtern, “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

[6] M. A. Naimark and A. I. Štern (Shtern), Theory of group representations, Grundlehren Math. Wiss., 246, Springer-Verlag, New York, 1982, ix+568 pp. | MR | Zbl

[7] I. Namioka, “Separate continuity and joint continuity”, Pacific J. Math., 51:2 (1974), 515–531 | DOI | MR | Zbl

[8] V. S. Varadarajan, Lie groups, Lie algebras, and their representations, Prentice-Hall Ser. Modern Anal., Prentice-Hall, Inc., Englewood Cliffs, NJ, 1974, xiii+430 pp. | DOI | MR | Zbl