Decomposition rank of approximately subhomogeneous C*-algebras
Operator Algebras
2020-03-12 v3
Abstract
It is shown that every Jiang-Su stable approximately subhomogeneous C*-algebra has finite decomposition rank. Previously, it was not even known that such algebras have finite nuclear dimension. A key step in the proof is that subhomogeneous C*-algebra are locally approximated by a certain class of more tractable subhomogeneous algebras, namely, a non-commutative generalization of the class of cell complexes. The result is applied to show that Jiang-Su stable minimal Z-crossed products have finite decomposition rank.
Keywords
Cite
@article{arxiv.1505.06100,
title = {Decomposition rank of approximately subhomogeneous C*-algebras},
author = {George A. Elliott and Zhuang Niu and Luis Santiago and Aaron Tikuisis},
journal= {arXiv preprint arXiv:1505.06100},
year = {2020}
}
Comments
86 pages. Fairly minor changes. To appear in Forum Math