Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results

Symmetry Integrability and Geometry-Methods and Applications

article

Raphaël Ponge¹ 

[1] School of Mathematics, Sichuan University

关键词: noncommutative residue;    canonical trace;    noncommutative tori;    pseudodifferential operators;   

DOI  :  10.3842/SIGMA.2020.061

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown