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Trudy Moskovskogo Matematicheskogo Obshchestva
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Trudy Moskovskogo Matematicheskogo Obshchestva, 2020, Volume 81, Issue 2, Pages 145–203 (Mi mmo639)  
This article is cited in 1 scientific paper (total in 1 paper)

Applications of noncommutative geometry in function theory and mathematical physics

A. G. Sergeev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (387 kB) Citations (1)
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Abstract: We review some applications of noncommutative geometry to function theory and mathematical physics. In the first case we discuss relations between the spaces of real variables and operator algebras. In the second case we deal with quantization of universal Techmüller space and quantum Hall effect.
Key words and phrases: operator calculus, Shatten–von Neumann classes, quantization of the universal Teichmüller space, quantum Hall effect.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00474
18-51-41011
18-51-05009
While preparing this paper the author was partially financially supported by the RFBR grants 19-01-00474, 18-51-41011, 18-51-05009.
Received: 11.04.2020
Revised: 29.04.2020
English version:
Transactions of the Moscow Mathematical Society, 2020, Volume 81, Issue 2, Pages 123–167
DOI: https://doi.org/10.1090/mosc/307
Bibliographic databases:
Document Type: Article
UDC: 517.986.9
MSC: 58B34, 81R60
Language: Russian
Citation: A. G. Sergeev, “Applications of noncommutative geometry in function theory and mathematical physics”, Tr. Mosk. Mat. Obs., 81, no. 2, MCCME, M., 2020, 145–203; Trans. Moscow Math. Soc., 81:2 (2020), 123–167
Citation in format AMSBIB
\Bibitem{Ser20}
\by A.~G.~Sergeev
\paper Applications of noncommutative geometry in function theory and mathematical physics
\serial Tr. Mosk. Mat. Obs.
\yr 2020
\vol 81
\issue 2
\pages 145--203
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo639}
\elib{https://elibrary.ru/item.asp?id=46761459}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2020
\vol 81
\issue 2
\pages 123--167
\crossref{https://doi.org/10.1090/mosc/307}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85103160875}
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  • https://www.mathnet.ru/eng/mmo639
  • https://www.mathnet.ru/eng/mmo/v81/i2/p145
    • This publication is cited in the following 1 articles:
    1. A. G. Sergeev, “On mathematical problems in the theory of topological insulators”, Theoret. and Math. Phys., 208:2 (2021), 1144–1155  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Trudy Moskovskogo Matematicheskogo Obshchestva
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    Abstract page:365
    Full-text PDF :125
    References:49
    First page:16
     
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