A construction method is presented for a class of simple C*-algebras whose basic properties -including their real ranks- can be computed relatively easily, using linear algebra. A numerival invariant attached to the construction determines wether a given algebra has real rank 0 or 1. Moreover, these algebras all have stable rank 1, and each nonzero hereditary sub-C*-algebra contains a nonzero projection, yet there are examples in which the linear span of the projections is not dense. (This phenomenon was first exhibited by Blackadar and Kumjian). The construction also produces easy examples of simple C*-algebras with real rank 0 and stable rank 1 for which K0 fails to be unperforated.
@article{urn:eudml:doc:41741,
title = {Notes on a class of simple C*-algebras with real rank zero.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {637-654},
mrnumber = {MR1209829},
zbl = {0812.46052},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41741}
}
Goodearl, Kenneth R. Notes on a class of simple C*-algebras with real rank zero.. Publicacions Matemàtiques, Tome 36 (1992) pp. 637-654. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41741/