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Purely infinite \(C^*\)-algebras from boundary actions of discrete groups. (English) Zbl 0863.46044
Sufficient conditions are given for an action of a discrete group on a locally compact space to yield a purely infinite \(C^*\)-algebra from the crossed product construction. Applications include the action of a word-hyperbolic group on the Gromov boundary, the Ruelle algebras associated to certain Smale spaces, and the action of \(\text{PSL}(n,\mathbb{Z})\) on a flag manifold.

MSC:
46L55 Noncommutative dynamical systems
46L35 Classifications of \(C^*\)-algebras
54H20 Topological dynamics (MSC2010)
57S25 Groups acting on specific manifolds
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