RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

 Mat. Sb., 2004, Volume 195, Number 9, Pages 145–159 (Mi msb849)

Criteria for the continuity of finite-dimensional representations of connected locally compact groups

A. I. Shtern

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Necessary and sufficient continuity conditions for finite-dimensional (not necessarily topological) representations of connected locally compact groups are obtained. Namely, it is shown that a finite-dimensional representation of a connected locally compact group is continuous if and only if the oscillation of this representation at the identity element of the group is less than 2.

DOI: https://doi.org/10.4213/sm849

Full text: PDF file (284 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2004, 195:9, 1377–1391

Bibliographic databases:

UDC: 512.546+517.987
MSC: Primary 22D12; Secondary 43A65, 47D03

Citation: A. I. Shtern, “Criteria for the continuity of finite-dimensional representations of connected locally compact groups”, Mat. Sb., 195:9 (2004), 145–159; Sb. Math., 195:9 (2004), 1377–1391

Citation in format AMSBIB
\Bibitem{Sht04} \by A.~I.~Shtern \paper Criteria for the continuity of finite-dimensional representations of~connected locally compact groups \jour Mat. Sb. \yr 2004 \vol 195 \issue 9 \pages 145--159 \mathnet{http://mi.mathnet.ru/msb849} \crossref{https://doi.org/10.4213/sm849} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2122373} \zmath{https://zbmath.org/?q=an:1075.22002} \elib{https://elibrary.ru/item.asp?id=14410837} \transl \jour Sb. Math. \yr 2004 \vol 195 \issue 9 \pages 1377--1391 \crossref{https://doi.org/10.1070/SM2004v195n09ABEH000849} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000226336000008} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-12144261044} 

• http://mi.mathnet.ru/eng/msb849
• https://doi.org/10.4213/sm849
• http://mi.mathnet.ru/eng/msb/v195/i9/p145

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Shtern A.I., “Van der Waerden continuity theorem for semisimple Lie groups”, Russ. J. Math. Phys., 13:2 (2006), 210–223
2. Shtern A.I., “Continuity conditions for finite-dimensional representations of some locally bounded groups”, Russ. J. Math. Phys., 13:4 (2006), 438–457
3. A. I. Shtern, “Automatic continuity of pseudocharacters on semisimple Lie groups”, Math. Notes, 80:3 (2006), 435–441
4. Shtern A.I., “Quasisymmetry. II”, Russ. J. Math. Phys., 14:3 (2007), 332–356
5. Shtern A.I., “Stability of the van der Waerden theorem on the continuity of homomorphisms of compact semisimple Lie groups”, Appl. Math. Comput., 187:1 (2007), 455–465
6. A. I. Shtern, “Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture”, J. Math. Sci., 159:5 (2009), 653–751
7. A. I. Shtern, “Kazhdan–Milman problem for semisimple compact Lie groups”, Russian Math. Surveys, 62:1 (2007), 113–174
8. 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
9. Shtern A.I., “Structure of finite-dimensional locally bounded finally precontinuous quasirepresentations of locally compact groups”, Russ. J. Math. Phys., 16:1 (2009), 133–138
10. Shtern I A., “Continuity Conditions For Finite-Dimensional Locally Bounded Representations of Connected Locally Compact Groups”, Russ. J. Math. Phys., 25:3 (2018), 345–382
•  Number of views: This page: 480 Full text: 115 References: 49 First page: 1