논문KCI 등재
Rigidity of the topology on the linear perfect connected Lie groups
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
주제분류수학
초록
In the paper, it is proved that every faithful locally bounded finite-dimensional representation of a perfect connected Lie group admitting sufficiently many locally bounded finite-dimensional representations (such a representation certainly exists) is a homeomorphism. In particular, the structure of bounded sets defines the topology for the groups in question.
Abstract
In the paper, it is proved that every faithful locally bounded finite-dimensional representation of a perfect connected Lie group admitting sufficiently many locally bounded finite-dimensional representations (such a representation certainly exists) is a homeomorphism. In particular, the structure of bounded sets defines the topology for the groups in question.
참고문헌 (8)
- A. I. Shtern, "Connected Lie groups with many locally bounded finite-dimensional representations are linear", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 14(2), pp.183~188 (2011), 장전수학회
- A. I. Shtern, "Van der Waerden's continuity theorem for the commutator subgroups of connected Lie groups and Mishchenko's conjecture", Advanced Studies in Contemporary Mathematics, 13(2), pp.143~158 (2006), 장전수학회
- A. I. Shtern, "A version of the van der Waerden theorem and the proof of the Mishchenko conjecture for homomorphisms of locally compact groups", Izv. Ross. Akad. Nauk Ser. Mat, 72(1), pp.183~224 (2008)
- Alexander I. Shtern, "APPLICATIONS OF AUTOMATIC CONTINUITY RESULTS TO ANALOGS OF THE FREUDENTHAL–WEIL AND HOCHSCHILD THEOREMS", Advanced Studies in Contemporary Mathematics, 20(2), pp.203~212 (2010), 장전수학회
- E. Hewitt, "Abstract Harmonic Analysis, Vol. I,In Structure of Topological Groups, Integration Theory, Group Representations" (1979), Springer
- M. Moskowitz, "Faithful representations and a local property of Lie groups", Math. Z, 143, pp.193~198 (1975)
- V. S. Varadarajan, "Lie Groups, Lie Algebras, and Their Representations" (1974), Prentice Hall
- P. B. Chen, "On a class of topological groups", Math. Ann, 266(4), pp.499~506 (1984)
관련 논문AI추천
Connected Lie groups with many locally bounded finite-dimensional representations are linearA. I. Shtern장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2011 · 제14권 제2호A 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 제1호Some almost connected locally compact groups whose group topology is determined by the bounded structureA. I. Shtern장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제2호Not necessarily continuous locally bounded finite-dimensional irreducible representations of connected lie groupsA. I. Shtern장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 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 제1호Not necessarily continuous locally bounded finite-dimensional representations of connected Lie groups with indecomposable restriction to the radicalA. I. Shtern장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제2호
이 간행물의 다른 논문 (10건)
A note on the modified q-Euler numbers and polynomials with weight김태균, 김영희, 최종성pp. 399-402An obvious proof of the perfect numbers conjectureIkorong Anouk Gilbert Nemronpp. 403-415A study on self-evaluation and peer-evaluation of teaching method in virtual mathematics lesson이상훈, T. Kim, 서종진pp. 417-433The uniqueness of the solutions for stochastic differential equations김영호pp. 435-445Exton’s triple hypergeometric series associated with the Kampé de Fériet function이창현, 김용섭pp. 447-453