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Trudy Mat. Inst. Steklova, 2010, Volume 271, Pages 204–223 (Mi tm3241)  

This article is cited in 3 scientific papers (total in 3 papers)

Noncommutative elliptic theory. Examples

A. Yu. Savinab, B. Yu. Sterninab

a Peoples' Friendship University of Russia, Moscow, Russia
b Leibniz Universität Hannover, Hannover, Germany

Abstract: We study differential operators with coefficients in noncommutative algebras. As an algebra of coefficients, we consider crossed products corresponding to the action of a discrete group on a smooth manifold. We give index formulas for the Euler, signature, and Dirac operators twisted by projections over the crossed product. The index of Connes operators on the noncommutative torus is computed.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 271, 193–211

Bibliographic databases:

UDC: 515.168.5+517.956.22
Received in December 2009

Citation: A. Yu. Savin, B. Yu. Sternin, “Noncommutative elliptic theory. Examples”, Differential equations and topology. II, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 204–223; Proc. Steklov Inst. Math., 271 (2010), 193–211

Citation in format AMSBIB
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\by A.~Yu.~Savin, B.~Yu.~Sternin
\paper Noncommutative elliptic theory. Examples
\inbook Differential equations and topology.~II
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2010
\vol 271
\pages 204--223
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3241}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2847766}
\elib{https://elibrary.ru/item.asp?id=15524642}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2010
\vol 271
\pages 193--211
\crossref{https://doi.org/10.1134/S0081543810040152}
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    This publication is cited in the following articles:
    1. A. Yu. Savin, B. Yu. Sternin, E. Schrohe, “On the index formula for an isometric diffeomorphism”, Journal of Mathematical Sciences, 201:6 (2014), 818–829  mathnet  crossref
    2. Dabrowski L., Sitarz A., “Curved Noncommutative Torus and Gauss-Bonnet”, J. Math. Phys., 54:1 (2013), 013518  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Savin A., Schrohe E., “Analytic and Algebraic Indices of Elliptic Operators Associated With Discrete Groups of Quantized Canonical Transformations”, J. Funct. Anal., 278:5 (2020), UNSP 108400  crossref  mathscinet  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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