Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Author: Ponge, Raphaël
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210787
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results. Raphaël Ponge. SIGMA 16 (2020), 061, 31 pages

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 a constant multiple of integer order pseudodifferential operators. The latter is...