Continuity criteria for locally bounded endomorphisms of central extensions of perfect Lie groups, Shtern A.Iстатья
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Дата последнего поиска статьи во внешних источниках: 1 мая 2024 г.
Аннотация:We prove that every locally bounded endomorphism,of a linear connected Lie central extension of a connected perfect Lie group, taking the center of the group into the center 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 Liegroup and the short sequence of Lie groups $\{e\}\to Z\to G\to H\to\{e\}$ is~exact, then every locally bounded endomorphism of~$G$ taking the center ofthe group into the center is continuous if and only if it is continuous on the center of~$G$.