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

This article is cited in 10 scientific papers (total in 10 papers)

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

Bibliographic databases:

UDC: 512.546+517.987
MSC: Primary 22D12; Secondary 43A65, 47D03
Received: 06.10.2003

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
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    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  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Shtern A.I., “Continuity conditions for finite-dimensional representations of some locally bounded groups”, Russ. J. Math. Phys., 13:4 (2006), 438–457  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. I. Shtern, “Automatic continuity of pseudocharacters on semisimple Lie groups”, Math. Notes, 80:3 (2006), 435–441  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Shtern A.I., “Quasisymmetry. II”, Russ. J. Math. Phys., 14:3 (2007), 332–356  crossref  mathscinet  zmath  isi  elib
    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  crossref  mathscinet  zmath  isi  elib
    6. A. I. Shtern, “Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture”, J. Math. Sci., 159:5 (2009), 653–751  mathnet  crossref  mathscinet  zmath  elib  elib
    7. A. I. Shtern, “Kazhdan–Milman problem for semisimple compact Lie groups”, Russian Math. Surveys, 62:1 (2007), 113–174  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    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  crossref  mathscinet  zmath  isi  elib
    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  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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