Covering Dimension for Nuclear C*-algebras
摘要
We introduce the completely positive rank, a notion of covering dimension for nuclear -algebras and analyze some of its properties. The completely positive rank behaves nicely with respect to direct sums, quotients, ideals and inductive limits. For abelian -algebras it coincides with covering dimension of the spectrum and there are similar results for continuous trace algebras. As it turns out, a -algebra is zero-dimensional precisely if it is . We consider various examples, particularly of one-dimensional -algebras, like the irrational rotation algebras, the Bunce-Deddens algebras or Blackadar's simple unital projectionless -algebra. Finally, we compare the completely positive rank to other concepts of noncommutative covering dimension, such as stable or real rank.
引用
@article{arxiv.math/0107218,
title = {Covering Dimension for Nuclear C*-algebras},
author = {Wilhelm Winter},
journal= {arXiv preprint arXiv:math/0107218},
year = {2007}
}