We describe the structure of ground states and ceiling states for generalized gauge actions on a UHF algebra. It is shown that both sets are affinely homeomorphic to the state space of a unital AF algebra, and that any pair of unital AF algebras can occur in this way, independently of the field of KMS states. In addition we study the subset of the ground states called \({\text {KMS}}_\infty \)-states.

中文翻译：

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UHF代数上的广义规范作用的基态

我们描述了UHF代数上广义规范行为的基态和上限状态的结构。结果表明，这两个集合对单位AF代数的状态空间是仿射同胚的，并且任何一对单位AF代数都可以这种方式出现，而与KMS状态域无关。此外，我们研究了称为\（{\ text {KMS}} _ \ infty \）- states的基态子集。