The bundle of KMS state spaces for flows on a unital C*-algebra
George A. Elliott, Klaus Thomsen
TL;DR
This paper demonstrates that any bundle of KMS state spaces associated with flows on certain C*-algebras can be realized on any given unital infinite-dimensional simple AF algebra, preserving the tracial state space structure.
Contribution
It shows the universality of AF algebras in realizing KMS state space bundles for flows with specified fiber structures.
Findings
Any bundle of KMS state spaces for a flow can be realized on a unital simple AF algebra.
The tracial state space of the AF algebra is affinely homeomorphic to the fiber over 0.
The construction applies to flows on unital separable C*-algebras with a trace state.
Abstract
It is shown that any bundle of KMS state spaces which can occur for a flow on a unital separable C*-algebra with a trace state can also be realized by a flow on any given unital infinite-dimensional simple AF algebra with a tracial state space affinely homeomorphic to the fiber in the bundle over 0.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Holomorphic and Operator Theory