On classification of non-unital amenable simple C*-algebras, III, the range and the reduction
Abstract
Following Elliott's earlier work, we show that the Elliott invariant of any finite separable simple -algebra with finite nuclear dimension can always be described as a scaled simple ordered group pairing together with a countable abelian group which unifies the unital and nonunital, as well as stably projectionless cases. We also show that, for any given such invariant set, there is a finite separable simple -algebra, whose Elliott invariant is the given set, a refinement of the range theorem of Elliott in the stable case. In the stably projectionless case, modified model -algebras are constructed in such a way that they are of generalized tracial rank one and have other technical features. We also show that every stably projectionless separable simple amenable -algebra in the UCT class has rationally generalized tracial rank one.
Cite
@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}
}
Comments
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