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Mat. Sb., 2010, Volume 201, Number 3, Pages 63–106 (Mi msb7537)  

This article is cited in 1 scientific paper (total in 1 paper)

On the index of noncommutative elliptic operators over $C^*$-algebras

A. Yu. Savinab, B. Yu. Sterninab

a Peoples Friendship University of Russia
b Leibniz University of Hannover

Abstract: We consider noncommutative elliptic operators over $C^*$-algebras, associated with a discrete group of isometries of a manifold. The main result of the paper is a formula expressing the Chern characters of the index (Connes invariants) in topological terms. As a corollary to this formula a simple proof of higher index formulae for noncommutative elliptic operators is obtained.
Bibliography: 36 titles.

Keywords: noncommutative elliptic operators, operators over $C^*$-algebras, index formulas, crossed product.

DOI: https://doi.org/10.4213/sm7537

Full text: PDF file (884 kB)
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English version:
Sbornik: Mathematics, 2010, 201:3, 377–417

Bibliographic databases:

UDC: 515.168.5+517.956.22
MSC: 19K56, 46L80, 58Jxx
Received: 07.02.2009 and 15.04.2009

Citation: A. Yu. Savin, B. Yu. Sternin, “On the index of noncommutative elliptic operators over $C^*$-algebras”, Mat. Sb., 201:3 (2010), 63–106; Sb. Math., 201:3 (2010), 377–417

Citation in format AMSBIB
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\yr 2010
\vol 201
\issue 3
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\crossref{https://doi.org/10.1070/SM2010v201n03ABEH004077}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Savin A.Yu., Sternin B.Yu., “An index formula for nonlocal operators corresponding to a diffeomorphism of a manifold”, Dokl. Math., 83:3 (2011), 353–356  crossref  mathscinet  zmath  isi  elib  elib  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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