English

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