On the Bundle of KMS State Spaces for Flows on a Z-Absorbing C*-Algebra
On the Bundle of KMS State Spaces for Flows on a Z-Absorbing C*-Algebra
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关于 Z 吸收 C* 代数上流的 KMS 状态空间丛
DOI：
10.1007/s00220-022-04386-x
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发表时间：
2022
影响因子：
2.4
通讯作者：
Klaus Thomsen
中科院分区：
文献类型：
--
作者：
George A. Elliott; Yasuhiko Sato;Klaus Thomsen
在逆温度集有界的情况下，给出了江苏C ~*-代数上流的KMS状态空间集的完整刻画。 也就是说，它是一个任意紧单纯形丛上的（紧）集的逆温度纤维在零一个单一的点。 （因此这适用于这个C*-代数与任何具有唯一迹态的单位C*-代数的张量积。一个类似的特征给出了任意流（Kirchberg-Phillips）可分类的无限单位单C*-代数：对于每个这样的代数的KMS状态形成一个任意适当的单纯形丛（逆温度的紧凑集的逆图像是紧凑的），使得纤维在零是空的。
A complete characterization is given of the collection of KMS state spaces for a flow on the Jiang-Su C*-algebra in the case that the set of inverse temperatures is bounded. Namely, it is an arbitrary compact simplex bundle over the (compact) set of inverse temperatures with fibre at zero a single point. (Hence this holds for the tensor product of this C*-algebra with any unital C*-algebra with unique trace state.) An analogous characterization is given for arbitrary flows on a (Kirchberg–Phillips) classifiable infinite unital simple C*-algebra: for each such algebra the KMS states form an arbitrary proper simplex bundle (the inverse image of a compact set of inverse temperatures is compact) such that the fibre at zero is empty.