An Introduction to KMS Weights

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.

- 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.

Klaus Erik Thomsen is emeritus professor at the university of Aarhus. He has published more than 100 papers on operator algebras, dynamical systems and K-theory. Twenty of his most recent papers are centered around the KMS condition.