论文标题
kms重量的简介
An introduction to KMS weights
论文作者
论文摘要
' KMS权重理论基于梳子和Kustermans定理的定理。在申请kms状态的unital $ c^*$ - 代数上，与稳定代数的KMS权重的关系已被证明很有用，并且这种关系取决于Laca和Neshveyev定理。前三章提供了这些基本结果的证据，这些结果需要最少的先决条件；特别是，它们不取决于冯·诺伊曼代数的模块化理论。相比之下，从第四章开始，所提出的材料在很大程度上借鉴了von Neumann代数的模块化理论。大多数结果是从N. V. Pedersen，J。Quaegebeur，J。Verding，J。Kustermans，S。Vaes，A。Kishimoto，A。Kumjian和J. Christensen的工作中得知的。在第九章和附录D和E中，读者可以找到作者最近获得的结果的介绍，部分是与G. A. Elliott和Y. Sato合作的。这种材料是Bratteli，Elliott，Herman和Kishimoto在1980年左右开发的方法的自然结晶。最后，在第十章中，对于KMS权重和状态的因素类型的概念简短。
' The theory of KMS weights is based on a theorem of Combes and a theorem of Kustermans. In applications to KMS states for flows on a unital $C^*$-algebra the relation to KMS weights of the stabilized algebra has proved useful and this relation hinges on a theorem of Laca and Neshveyev. The first three chapters present proofs of these fundamental results that require a minimum of prerequisites; in particular, they do not depend on the modular theory of von Neumann algebras. In contrast, starting with chapter four the presented material draws heavily on the modular theory of von Neumann algebras. Most results are known from the work of N. V. Pedersen, J. Quaegebeur, J. Verding, J. Kustermans, S. Vaes, A. Kishimoto, A. Kumjian and J. Christensen, but new ones begin to surface. In chapter nine and the Appendices D and E the reader can find a presentation of results obtained recently by the author, partly in collaboration with G. A. Elliott and Y. Sato. This material is a natural culmination of methods developed around 1980 by Bratteli, Elliott, Herman and Kishimoto. Finally, in chapter ten there is a short presentation of the notion of factor types for KMS weights and states.
