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.
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
\Bibitem{Ser17}
\by A.~G.~Sergeev
\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
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 298
\pages 276--314
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968517030177}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2017
\vol 298
\pages 256--293
\crossref{https://doi.org/10.1134/S0081543817060177}
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https://www.mathnet.ru/eng/tm3806
https://doi.org/10.1134/S0371968517030177
https://www.mathnet.ru/eng/tm/v298/p276
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