This book provides an introduction to the theory of KMS weights and KMS states, which play an important role in mathematical physics and other applications of operator algebras. Leading from the definitions to some of the most recent research results, it covers advanced topics such as the Laca-Neshveyev theorem, elements of the modular theory of von Neumann algebras, the geometry of the set of KMS weights, duality (for KMS weights on crossed products), the relationship between KMS weights and traces and the types of factors associated with extremal KMS weights. Some of the material is new, in the sense that the proofs and results are published here for the first time. This relatively self-contained book will be useful both to researchers in the area of operator algebras and to more advanced students who wish to enter this field.
Inhaltsverzeichnis
- 1. Weights. - 2. KMS Weights. - 3. Laca-Neshveyev Theorem. - 4. Modular Theory. - 5. The Set of -KMS Weights. - 6. Some Examples and Constructions. - 7. Dual KMS Weights. - 8. On Tracial Representations of KMS Weights. - 9. The Bundle of KMS States. - 10. Factor Types of Extremal KMS Weights.
This book offers a structured introduction to the subject, presenting its core concepts and main results. The book is self-contained and accessible to readers with a standard background in C*-algebras and von Neumann algebras, providing a solid foundation for engaging with the subject. This work serves as a valuable resource for experienced researchers, extending beyond the scope of standard textbooks, while also offering an excellent introduction to the topic. (Evgenios Kakariadis, zbMATH 1569. 46001, 2026)
The book has ten chapters and five appendices. . . . this book can serve as an introduction to the theory of KMS weights and KMS states, while it also leads to more advanced topics and presents some new results. It will be a useful resource for the research community working in this area and related topics. (Xin Li, Mathematical Reviews, October, 2025)
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