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Commutative \(C^*\)-subalgebras of simple stably finite \(C^*\)-algebras with real rank zero. (English) Zbl 1173.46041

Summary: Let \(X\) be a second countable, path connected, compact metric space and let \(A\) be a unital separable simple nuclear \({\mathcal Z}\)-stable real rank zero \(C^*\)-algebra. We classify all the unital *-embeddings (up to approximate unitary equivalence) of \(C(X)\) into \(A\). Specifically, we provide an existence and a uniqueness theorem for unital *-embeddings from \(C(X)\) into \(A\).

MSC:

46L35 Classifications of \(C^*\)-algebras
46L80 \(K\)-theory and operator algebras (including cyclic theory)