Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 061, 31 pages      arXiv:1911.12164
Contribution to the Special Issue on Noncommutative Manifolds and their Symmetries in honour of Giovanni Landi

Noncommutative Residue and Canonical Trace on Noncommutative Tori. Uniqueness Results

Raphaël Ponge
School of Mathematics, Sichuan University, Chengdu, China

Received January 09, 2020, in final form June 15, 2020; Published online July 05, 2020

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.

Key words:noncommutative residue; canonical trace; noncommutative tori; pseudodifferential operators.

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