Purely infinite C*-algebras arising from crossed products
Research output: Contribution to journal › Journal article › Research › peer-review
We study conditions that will ensure that a crossed product
of a C-algebra by a discrete exact group is purely innite (simple or
non-simple). We are particularly interested in the case of a discrete nonamenable
exact group acting on a commutative C-algebra, where our
sucient conditions can be phrased in terms of paradoxicality of subsets
of the spectrum of the abelian C-algebra.
As an application of our results we show that every discrete countable
non-amenable exact group admits a free amenable minimal action on the
Cantor set such that the corresponding crossed product C-algebra is a
Kirchberg algebra in the UCT class.
of a C-algebra by a discrete exact group is purely innite (simple or
non-simple). We are particularly interested in the case of a discrete nonamenable
exact group acting on a commutative C-algebra, where our
sucient conditions can be phrased in terms of paradoxicality of subsets
of the spectrum of the abelian C-algebra.
As an application of our results we show that every discrete countable
non-amenable exact group admits a free amenable minimal action on the
Cantor set such that the corresponding crossed product C-algebra is a
Kirchberg algebra in the UCT class.
Original language | English |
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Journal | Ergodic Theory and Dynamical Systems |
Volume | 32 |
Pages (from-to) | 273-293 |
Number of pages | 21 |
ISSN | 0143-3857 |
Publication status | Published - 2012 |
ID: 22796693