Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 137, Pages 61–81 (Mi into205)  
This article is cited in 1 scientific paper (total in 1 paper)

Noncommutative geometry and analysis

A. G. Sergeev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (293 kB) Citations (1)
Abstract: One of the main problems of noncommutative geometry is the translation of fundamental notions of analysis, topology, and differential geometry onto the language of Banach algebras. In this paper, we present a number of results of this kind focusing the attention on the noncommutative interpretation of the notions of differential and integral. Our presentation is based on the monographs Noncommutative Geometry by A. Connes and Elements of Noncommutative Geometry by J. M. Gracia-Bondia, J. C. Varilly, and H. Figueroa.
Keywords: $C^*$-algebra, Dixmier trace, Wodzicki residue, differential graded algebra, cycle, Fredholm module, Chern cocycle.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00117
16-52-12012
Ministry of Education and Science of the Russian Federation НШ-9110.2016.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations Нелинейная динамика
This work is supported by the Russian Foundation for Basic Research (project Nos. 16-01-00117 and 16-52-12012), the Program for Support of Leading Scientific Schools (project No. NSh-9110.2016.1), and the Program of the Presidium of the Russian Academy of Sciences “Nonlinear Dynamics.”
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 236, Issue 6, Pages 641–662
DOI: https://doi.org/10.1007/s10958-018-4137-x
Bibliographic databases:
Document Type: Article
UDC: 517.986.32
MSC: 47L30
Language: Russian
Citation: A. G. Sergeev, “Noncommutative geometry and analysis”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 137, VINITI, Moscow, 2017, 61–81; J. Math. Sci. (N. Y.), 236:6 (2019), 641–662
Citation in format AMSBIB
\Bibitem{Ser17}
\by A.~G.~Sergeev
\paper Noncommutative geometry and analysis
\inbook Differential equations. Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 137
\pages 61--81
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into205}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801260}
\zmath{https://zbmath.org/?q=an:07058890}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 236
\issue 6
\pages 641--662
\crossref{https://doi.org/10.1007/s10958-018-4137-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85059483462}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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