On higher real and stable ranks for CCR C*-algebras
Abstract
We calculate the real rank and stable rank of CCR algebras which either have only finite dimensional irreducible representations or have finite topological dimension. We show that either rank of A is determined in a good way by the ranks of an ideal I and the quotient A/I in four cases: When A is CCR; when I has only finite dimensional irreducible representations; when I is separable, of generalized continuous trace and finite topological dimension, and all irreducible representations of I are infinite dimensional; or when I is separable, stable, has an approximate identity consisting of projections, and has the corona factorization property. We also present a counterexample on higher ranks of M(A), A subhomogeneous, and a theorem of P. Green on generalized continuous trace algebras.
Keywords
Cite
@article{arxiv.0708.3072,
title = {On higher real and stable ranks for CCR C*-algebras},
author = {Lawrence G. Brown},
journal= {arXiv preprint arXiv:0708.3072},
year = {2017}
}
Comments
I intend to submit a revised version of this paper, reflecting comments received, in September and will replace it with the submitted version at that time