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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 298, Pages 276–314
DOI: https://doi.org/10.1134/S0371968517030177 (Mi tm3806) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Spin Geometry of Dirac and Noncommutative Geometry of Connes

A. G. Sergeev

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (384 kB) Citations (4)
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DOI: https://doi.org/10.1134/S0371968517030177
Abstract: The review is devoted to the interpretation of the Dirac spin geometry in terms of noncommutative geometry. In particular, we give an idea of the proof of the theorem stating that the classical Dirac geometry is a noncommutative spin geometry in the sense of Connes, as well as an idea of the proof of the converse theorem stating that any noncommutative spin geometry over the algebra of smooth functions on a smooth manifold is the Dirac spin geometry.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.
Received: December 11, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 298, Pages 256–293
DOI: https://doi.org/10.1134/S0081543817060177
Bibliographic databases:
Document Type: Article
UDC: 514.74
Language: Russian
Citation: A. G. Sergeev, “Spin Geometry of Dirac and Noncommutative Geometry of Connes”, Complex analysis and its applications, Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar, Trudy Mat. Inst. Steklova, 298, MAIK Nauka/Interperiodica, Moscow, 2017, 276–314; Proc. Steklov Inst. Math., 298 (2017), 256–293
Citation in format AMSBIB
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\paper Spin Geometry of Dirac and Noncommutative Geometry of Connes
\inbook Complex analysis and its applications
\bookinfo Collected papers. On the occasion of the centenary of the birth of Boris Vladimirovich Shabat, 85th anniversary of the birth of Anatoliy Georgievich Vitushkin, and 85th anniversary of the birth of Andrei Aleksandrovich Gonchar
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\pages 276--314
\publ MAIK Nauka/Interperiodica
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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