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Sbornik: Mathematics, 2010, Volume 201, Issue 3, Pages 377–417
DOI: https://doi.org/10.1070/SM2010v201n03ABEH004077 (Mi sm7537) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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
English version PDF (583 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM2010v201n03ABEH004077
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.
Received: 07.02.2009 and 15.04.2009
Russian version:
Matematicheskii Sbornik, 2010, Volume 201, Number 3, Pages 63–106
DOI: https://doi.org/10.4213/sm7537
Bibliographic databases:
UDC: 515.168.5+517.956.22
MSC: 19K56, 46L80, 58Jxx
Language: English
Original paper language: Russian
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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  • https://doi.org/10.1070/SM2010v201n03ABEH004077
  • https://www.mathnet.ru/eng/sm/v201/i3/p63
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:9
    References:54
    First page:5
     
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