Homogeneity of the pure state space of a separable C*-algebra
classification
🧮 math.OA
keywords
algebraspureseparablespacestateactionalgebraasymptotically
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We prove that the pure state space is homogeneous under the action of the automorphism group (or the subgroup of asymptotically inner automorphisms) for all the separable simple C*-algebras. The first result of this kind was shown by Powers for the UHF algebras some 30 years ago.
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