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

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
\Bibitem{Sht07} \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 \mathnet{http://mi.mathnet.ru/fpm1096} \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
2. Shtern A.I., “Almost periodic functions on connected locally compact groups”, Russ. J. Math. Phys., 17:4 (2010), 509–510
3. Shtern A.I., “Von Neumann kernels of connected Lie groups, revisited and refined”, Russ. J. Math. Phys., 17:2 (2010), 262–266
4. A. I. Shtern, “The structure of homomorphisms of connected locally compact groups into compact groups”, Izv. Math., 75:6 (2011), 1279–1304
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
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
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
8. Shtern A.I., “Continuity Conditions for Finite-Dimensional Representations of Connected Locally Compact Groups”, Russ. J. Math. Phys., 19:4 (2012), 499–501
9. Shtern A.I., “Properties of Pseudocharacters on Connected Locally Compact Groups”, Russ. J. Math. Phys., 21:2 (2014), 291–293
10. Dadarlat M., “Group Quasi-Representations and Almost Flat Bundles”, J. Noncommutative Geom., 8:1 (2014), 163–178
11. Shtern A.I., “a Freudenthal-Weil Theorem For Pro-Lie Groups”, Russ. J. Math. Phys., 22:4 (2015), 546–549
12. A. I. Shtern, “Specific properties of one-dimensional pseudorepresentations of groups”, J. Math. Sci., 233:5 (2018), 770–776
13. A. I. Shtern, “Locally bounded finally precontinuous finite-dimensional quasirepresentations of connected locally compact groups”, Sb. Math., 208:10 (2017), 1557–1576
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
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
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