非单位元顺从单C*-代数的分类,III,值域与约化
算子代数
2022-09-14 v4
摘要
继Elliott早前工作,我们证明任意具有有限核维数的有限可分单 -代数的Elliott不变量总可描述为带尺度的简单有序群配对连同可数阿贝尔群,这统一了单位元与非单位元以及稳定无投影情形。我们还证明,对任意给定的此类不变量集合,存在一个有限可分单 -代数,其Elliott不变量为该给定集合,这是Elliott稳定情形值域定理的精细化。在稳定无投影情形,我们构造了修正的模型 -代数,使其具有广义迹秩一及其他技术特征。我们还证明UCT类中的任意稳定无投影可分单顺从 -代数具有有理广义迹秩一。
引用
@article{arxiv.2010.01788,
title = {On classification of non-unital amenable simple C*-algebras, III, the range and the reduction},
author = {Huaxin Lin and Guihua Gong},
journal= {arXiv preprint arXiv:2010.01788},
year = {2022}
}
备注
193 pages, the revision removes the condition of stable rank one in the main theorem (it has been divided into two papers). 2021/12: This is the first part of the original paper. The second part of the revision is also ready and we will try to post it at the same time