Homogeneity of the Pure State Space of a Separable ${{C}^{*}}$ -Algebra

By A. Kishimoto, Nathanial P. Brown Narutaka Ozawa, S. Sakai. Canadian mathematical bulletin, 2001

58 citations recorded by the source corpus.

Abstract 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 $\text{UHF}$ algbras some 30 years ago.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ca6524eda2214c9d173a43ae603f068ba4e16878

Citations in the corpus

• Divisibility properties for C*‐algebras (2011, unknown): “visibility of a C∗-algebra can be interpreted as a degree of inhomogeneity (or “lumpiness”) of the C∗-algebra. Simple C∗-algebras are sometimes thought of as being very homogeneous, as for example in [KOS03]. From this point of view it may at first be surprising that a simple infinite dimensional C∗-a”
• Turbulence, orbit equivalence, and the classification of nuclear C*-algebras (2011, unknown): “ote the vector state corresponding to ξ, ωξ(a) = (aξ|ξ). Since Ais weakly dense in B(H), the restriction of ωξto Ais a pure state of A, and similarly the restriction of ωξto Bis a pure state of B. By [18] there is an automorphism βof Bsuch that ωξ↾ B= β◦α◦ωξ. 34 ILIJAS FARAH, ANDREW S. TOMS AND ASGE”