논문KCI 등재
LOCALLY BOUNDED AUTOMORPHISMS OF CONNECTED LIE GROUPS WITHOUT NONTRIVIAL COMPACT CONNECTED SUBGROUPS
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참고문헌
키워드
주제분류수학
초록
It is proved that every locally bounded automorphism of a connected Lie group without nontrivial compact connected subgroups is continuous. In particular, every locally bounded automorphism of the universal covering group of the real unimodular group of 2 × 2 matrices is continuous.
Abstract
It is proved that every locally bounded automorphism of a connected Lie group without nontrivial compact connected subgroups is continuous. In particular, every locally bounded automorphism of the universal covering group of the real unimodular group of 2 × 2 matrices is continuous.
참고문헌 (5)
- 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), pp.169~205 (2008)
- A. I. Shtern, "Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko’s conjecture", J. Math. Sci. (N. Y.), 159(5), pp.653~751 (2009)
- A. I. Shtern, "Locally Bounded Finally Precontinuous Finite-Dimensional Quasirepresentations of Locally Compact Groups", Sb. Math, 208(10), pp.1557~1576 (2017)
- V. S. Varadarajan, "Lie Groups, Lie Algebras, and Their Representations" (1974), Prentice-Hall Inc.
- A. I. Shtern, "Locally bounded automorphisms of connected reductive Lie groups", Russ. J. Math. Phys, 28(3), pp.356~357 (2021)
관련 논문AI추천
Locally bounded automorphisms of connected Lie groupsA. I. Shtern장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2025 · 제28권 제3호Continuity conditions for homomorphisms of connected locally compact groups into Lie groupsA. I. Shtern장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2025 · 제28권 제2호LOCALLY BOUNDED NOT A PRIORI CONTINUOUS HOMOMORPHISMS OF NONCOMPACT SEMISIMPLE LIE GROUPS INTO CONNECTED AMENABLE LIE GROUPS ARE IDENTITY HOMOMORPHISMSA. I. SHTERN장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제3호A criterion for the continuity of the restriction to the commutator subgroup of a locally bounded finite-dimensional representation of a connected Lie group with respect to the ordinary group topologyA. I. Shtern장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제1호IMPROVED CONTINUITY CRITERIA FOR LOCALLY BOUNDED HOMOMORPHISMS BETWEEN CENTRAL EXTENSIONS OF PERFECT LIE GROUPSA. I. Shtern장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2024 · 제27권 제1호Bounded structure and continuity for homomorphisms of perfect connected locally compact groupsA. I. Shtern장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2012 · 제15권 제3호
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