The canonical trace and the noncommutative residue on the noncommutative torus

DOI10.1090/tran/6369zbMath1337.58005arXiv1303.0241OpenAlexW2140352571MaRDI QIDQ2796515

Carolina Neira Jiménez, Sylvie Paycha, Cyril Levy

Publication date: 29 March 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.0241

zbMATH Keywords

pseudodifferential operatorsnoncommutative tori

Mathematics Subject Classification ID

Noncommutative topology (46L85) Noncommutative geometry (à la Connes) (58B34) Noncommutative global analysis, noncommutative residues (58J42)

Related Items (17)

Quantum Euclidean spaces with noncommutative derivatives ⋮ Local and global symbols on compact Lie groups ⋮ Smooth dense subalgebras and Fourier multipliers on compact quantum groups ⋮ A noncommutative Tauberian theorem and Weyl asymptotics in noncommutative geometry ⋮ Spectral metric and Einstein functionals ⋮ Functional calculus for elliptic operators on noncommutative tori. I ⋮ Connes’s trace theorem for curved noncommutative tori: Application to scalar curvature ⋮ Gravity, non-commutative geometry, and the Wodzicki residue ⋮ Quantum differentiability on quantum tori ⋮ Difference equations and pseudo-differential operators on \(\mathbb{Z}^n\) ⋮ Pseudodifferential calculus on noncommutative tori, I. Oscillating integrals ⋮ Pseudodifferential calculus on noncommutative tori, II. Main properties ⋮ Mapping properties of operator-valued pseudo-differential operators ⋮ Noncommutative residue and canonical trace on noncommutative tori. Uniqueness results ⋮ Real trace expansions ⋮ On the scalar curvature for the noncommutative four torus ⋮ Dixmier trace formulas and negative eigenvalues of Schrödinger operators on curved noncommutative tori

Cites Work

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• The noncommutative residue for manifolds with boundary
• The Gauss-Bonnet Theorem for the noncommutative two torus
• Noncommutative Geometry and Global Analysis
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• On the Fourier Analysis of Operators on the Torus
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• Characterizations of pseudodifferential operators on the circle
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• Uniqueness of the Kontsevich-Vishik trace
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