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.
\Bibitem{SavSte10}
\by A.~Yu.~Savin, B.~Yu.~Sternin
\paper On the index of noncommutative elliptic operators over $C^*$-algebras
\jour Sb. Math.
\yr 2010
\vol 201
\issue 3
\pages 377--417
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Linking options:
https://www.mathnet.ru/eng/sm7537
https://doi.org/10.1070/SM2010v201n03ABEH004077
https://www.mathnet.ru/eng/sm/v201/i3/p63
This publication is cited in the following 3 articles:
Boltachev V A., Savin A.Yu., “Elliptic Boundary Value Problems Associated With Isometric Group Actions”, J. Pseudo-Differ. Oper. Appl., 12:4 (2021), 50
Anton Savin, Boris Sternin, Pseudo-Differential Operators, Generalized Functions and Asymptotics, 2013, 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
Citation in format AMSBIB
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