Measure Theory in Noncommutative Spaces

Symmetry Integrability and Geometry-Methods and Applications

article

Steven Lord¹  Fedor Sukochev² 

[1] School of Mathematical Sciences, University of Adelaide;School of Mathematics and Statistics, University of New South Wales

关键词: Dixmier trace;    singular trace;    noncommutative integration;    noncommutative geometry;    Lebesgue integral;    noncommutative residue;   

DOI  :  10.3842/SIGMA.2010.072

来源: National Academy of Science of Ukraine

【 摘 要 】

The integral in noncommutative geometry (NCG) involves a non-standard trace called a Dixmier trace. The geometric origins of this integral are well known. From a measure-theoretic view, however, the formulation contains several difficulties. We review results concerning the technical features of the integral in NCG and some outstanding problems in this area. The review is aimed for the general user of NCG.

【 授权许可】

Unknown