We study certain principal actions on noncommutative C*-algebras. Our main examples are the - and -actions on the odd-dimensional quantum spheres, yielding as fixed-point algebras quantum lens spaces and quantum complex projective spaces, respectively. The key tool in our analysis is the relation of the ambient C*-algebras with the Cuntz-Krieger algebras of directed graphs. A general result about the principality of the gauge action on graph algebras is given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-18,
author = {Wojciech Szyma\'nski},
title = {Quantum lens spaces and principal actions on graph C*-algebras},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {299-304},
zbl = {1067.46067},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-18}
}
Wojciech Szymański. Quantum lens spaces and principal actions on graph C*-algebras. Banach Center Publications, Tome 60 (2003) pp. 299-304. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-18/