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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.
† Author to whom correspondence should be addressed
DOI:
https://doi.org/10.4213/sm7537
 Full text:
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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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Linking options:
http://mi.mathnet.ru/eng/msb7537https://doi.org/10.4213/sm7537 http://mi.mathnet.ru/eng/msb/v201/i3/p63
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This publication is cited in the following articles:
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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
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