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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 061, 31 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.061 (Mi sigma1598) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results

Raphaël Ponge

School of Mathematics, Sichuan University, Chengdu, China
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DOI: https://doi.org/10.3842/SIGMA.2020.061
Abstract: In this paper we establish uniqueness theorems for the noncommutative residue and the canonical trace on pseudodifferential operators on noncommutative tori of arbitrary dimension. The former is the unique trace up to constant multiple on integer order pseudodifferential operators.The latter is the unique trace up to constant multiple on non-integer order pseudodifferential operators. This improves previous uniqueness results by Fathizadeh–Khalkhali, Fathizadeh–Wong, and Lévy–Neira–Paycha.
Keywords: noncommutative residue, canonical trace, noncommutative tori, pseudodifferential operators.
Funding agency Grant number
National Natural Science Foundation of China 11971328
The research for this article was partially supported by the NSFC under Grant No. 11971328 (China).
Received: January 9, 2020; in final form June 15, 2020; Published online July 5, 2020
Bibliographic databases:
Document Type: Article
MSC: 58J42, 58B34, 58J40
Language: English
Citation: Raphaël Ponge, “Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results”, SIGMA, 16 (2020), 061, 31 pp.
Citation in format AMSBIB
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