A. I. Shtern, “Automatic continuity of a locally bounded homomorphism of Lie groups on the commutator subgroup”, Mat. Sb., 2024, Volume 215, Number 6,Pages <nobr>151

Automatic continuity of a locally bounded homomorphism of Lie groups on the commutator subgroup

A. I. Shtern^abc

^a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^b Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
^c Scientific Research Institute for System Studies of the Russian Academy of Sciences, Moscow, Russia

Abstract: 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: Lie group homomorphism, locally bounded homomorphism, discontinuity group of a homomorphism, commutator subgroup.

PACS: 02.20.Qs

MSC: 22A25

Received: 23.07.2023 and 26.12.2023

DOI: 10.4213/sm9984