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Fundam. Prikl. Mat., 2007, Volume 13, Issue 7, Pages 85–225 (Mi fpm1096)  

This article is cited in 15 scientific papers (total in 15 papers)

Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture

A. I. Shtern

M. V. Lomonosov Moscow State University

Abstract: In this paper, a description of the structure of all finite-dimensional, locally bounded quasirepresentations of arbitrary connected Lie groups is given and the proof of Mishchenko's conjecture for connected, locally compact groups and a proof of an analog of the van der Waerden theorem (i.e., the automatic continuity condition for all locally bounded, finite-dimensional representations) for the commutator subgroup of an arbitrary connected Lie group are presented.

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English version:
Journal of Mathematical Sciences (New York), 2009, 159:5, 653–751

Bibliographic databases:

UDC: 512.546+517.986.6+512.815.1

Citation: A. I. Shtern, “Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture”, Fundam. Prikl. Mat., 13:7 (2007), 85–225; J. Math. Sci., 159:5 (2009), 653–751

Citation in format AMSBIB
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\by A.~I.~Shtern
\paper Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture
\jour Fundam. Prikl. Mat.
\yr 2007
\vol 13
\issue 7
\pages 85--225
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2475577}
\zmath{https://zbmath.org/?q=an:1187.22014}
\elib{http://elibrary.ru/item.asp?id=11162707}
\transl
\jour J. Math. Sci.
\yr 2009
\vol 159
\issue 5
\pages 653--751
\crossref{https://doi.org/10.1007/s10958-009-9466-3}
\elib{http://elibrary.ru/item.asp?id=13615662}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67349113529}


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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. A. I. Shtern, “Duality between compactness and discreteness beyond Pontryagin duality”, Proc. Steklov Inst. Math., 271 (2010), 212–227  mathnet  crossref  mathscinet  isi  elib
    2. Shtern A.I., “Almost periodic functions on connected locally compact groups”, Russ. J. Math. Phys., 17:4 (2010), 509–510  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Shtern A.I., “Von Neumann kernels of connected Lie groups, revisited and refined”, Russ. J. Math. Phys., 17:2 (2010), 262–266  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. A. I. Shtern, “The structure of homomorphisms of connected locally compact groups into compact groups”, Izv. Math., 75:6 (2011), 1279–1304  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Shtern A.I., “Hochschild kernel for locally bounded finite-dimensional representations of a connected Lie group”, Appl. Math. Comput., 218:3 (2011), 1063–1066  crossref  mathscinet  zmath  isi  elib
    6. Shtern A.I., “Alternative proof of the Hochschild triviality theorem for a connected locally compact group”, Russ. J. Math. Phys., 18:1 (2011), 102–106  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. A. I. Shtern, “Connected locally compact groups: The Hochschild kernel and faithfulness of locally bounded finite-dimensional representations”, Trans. Moscow Math. Soc., 72 (2011), 79–95  mathnet  crossref  zmath  elib
    8. Shtern A.I., “Continuity Conditions for Finite-Dimensional Representations of Connected Locally Compact Groups”, Russ. J. Math. Phys., 19:4 (2012), 499–501  crossref  mathscinet  zmath  isi  elib
    9. Shtern A.I., “Properties of Pseudocharacters on Connected Locally Compact Groups”, Russ. J. Math. Phys., 21:2 (2014), 291–293  crossref  mathscinet  zmath  isi  elib
    10. Dadarlat M., “Group Quasi-Representations and Almost Flat Bundles”, J. Noncommutative Geom., 8:1 (2014), 163–178  crossref  mathscinet  zmath  isi  elib
    11. Shtern A.I., “a Freudenthal-Weil Theorem For Pro-Lie Groups”, Russ. J. Math. Phys., 22:4 (2015), 546–549  crossref  mathscinet  zmath  isi
    12. A. I. Shtern, “Specific properties of one-dimensional pseudorepresentations of groups”, J. Math. Sci., 233:5 (2018), 770–776  mathnet  crossref
    13. A. I. Shtern, “Locally bounded finally precontinuous finite-dimensional quasirepresentations of connected locally compact groups”, Sb. Math., 208:10 (2017), 1557–1576  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    14. Shtern A.I., “Representations Associated to Quasirepresentations of Amenable Groups With Zero Multiplication of Defect Operators”, Russ. J. Math. Phys., 24:3 (2017), 373–375  crossref  mathscinet  zmath  isi  scopus
    15. 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
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