Equilibrium states and fine structure for operator algebras

这个项目是在纯数学，在广泛的领域的功能分析，并特别侧重于算子代数。算子代数上的Kubo-Martin-Schwinger（KMS）态编码C*-代数动力系统的平衡。该项目的目的是采取一种新的观点KMS数据作为一个仓库的精细运营商代数结构。它旨在发展一种理论，使KMS状态恢复结构细节，如连续理想结构和简单性。该项目预计将确定在何种程度上的KMS单纯形的组合算子代数记住潜在的组合数据。它还旨在探索组合算子代数上的KMS态，作为现代算子代数理论两个主要分支之间相互作用的新点。

This project is in pure mathematics, in the broad area of functional analysis, and focuses specifically on operator algebras. Kubo-Martin-Schwinger (KMS) states on operator algebras encode equilibria of C*-algebraic dynamical systems. This project aims to take a novel view of KMS data as a repository of fine operator-algebraic structure. It aims to develop a theory whereby KMS states recover structural details like primitive-ideal structure and simplicity. The project is expected to determine to what extent the KMS simplex of combinatorial operator algebra remembers underlying combinatorial data. It also aims to explore KMS states on combinatorial operator algebras as a new point of interaction between the two main branches of modern operator-algebra theory.