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Characterizations of topological dynamical systems whose transformation group \(C^*\)-algebras are antiliminal and of type 1. (English) Zbl 0808.54031

Summary: For a topological dynamical system \(\Sigma = (X, \sigma)\) where \(X\) is a compact metric space with a single homeomorphism \(\sigma\), we determine the largest postliminal ideal of the transformation group \(C^*\)-algebra \(A (\Sigma)\) as the intersection of all kernels of irreducible representations of \(A (\Sigma)\) induced from those recurrent points which are not periodic. The result implies characterizations of topological dynamical systems whose transformation group \(C^*\)-algebras are anti- liminal and post-liminal, that is, of type 1.

MSC:

54H20 Topological dynamics (MSC2010)
46L55 Noncommutative dynamical systems
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