Abstract:
The notion of a generic curved noncommutative torus is considered, which extends the notion of conformally deformed noncommutative torus introduced by Connes and Tretkoff. For this manifold, an asymptotic expansion is established for the heat semigroup generated by Laplace–Beltrami operator (in fact, for an arbitrary selfadjoint positive elliptic differential operator of order $2$) and an algorithm is provided to compute the local invariants that arize as coefficients in the expansion. This allows one to extend a series of previous results by several authors beyond the conformal case and/or for multidimensional tori.
Citation:
F. Sukochev, D. Zanin, “Local invariants of noncommutative tori”, Algebra i Analiz, 35:2 (2023), 174–225; St. Petersburg Math. J., 35:2 (2024), 377–415
\Bibitem{SukZan23}
\by F.~Sukochev, D.~Zanin
\paper Local invariants of noncommutative tori
\jour Algebra i Analiz
\yr 2023
\vol 35
\issue 2
\pages 174--225
\mathnet{http://mi.mathnet.ru/aa1862}
\transl
\jour St. Petersburg Math. J.
\yr 2024
\vol 35
\issue 2
\pages 377--415
\crossref{https://doi.org/10.1090/spmj/1808}
Linking options:
https://www.mathnet.ru/eng/aa1862
https://www.mathnet.ru/eng/aa/v35/i2/p174
This publication is cited in the following 2 articles:
J. Huang, Y. Nessipbayev, F. Sukochev, D. Zanin, “Compactness criteria in quasi-Banach symmetric operator spaces associated with a non-commutative torus”, Journal of Functional Analysis, 2025, 110946
Teun van Nuland, Fedor Sukochev, Dmitriy Zanin, “Local invariants of conformally deformed non-commutative tori II: multiple operator integrals”, Journal of Functional Analysis, 2024, 110754
Citation in format AMSBIB
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