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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 137, Pages 61–81
(Mi into205)
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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
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.
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
Linking options:
https://www.mathnet.ru/eng/into205 https://www.mathnet.ru/eng/into/v137/p61
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Abstract page: | 602 | Full-text PDF : | 293 | First page: | 37 |
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