Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results

被引：5

作者：

Ponge, Raphael ^{[1
]}

机构：

[1] Sichuan Univ, Sch Math, Chengdu, Peoples R China

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2020年 / 16卷

关键词：

noncommutative residue; canonical trace; noncommutative tori; pseudodifferential operators; C-STAR-ALGEBRAS; MODULAR CURVATURE; CROSSED-PRODUCTS; PSEUDODIFFERENTIAL-OPERATORS; SCALAR CURVATURE; DETERMINANTS; MANIFOLDS; CALCULUS; FORMULA;

D O I：

10.3842/SIGMA.2020.061

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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 Levy-Neira-Paycha.

引用

页数：31

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