Edinburgh University Press eBooks· 2020· Book chapter
Modular Theory in Operator Algebras
- 485citations
- 2020year
Short summary
This revised edition of a foundational 1981 text offers a comprehensive monograph on operator algebras, covering fundamentals and recent advancements for students and researchers in mathematics, physics, and related fields.
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Key points
- Revised edition of a seminal 1981 monograph on operator algebras.
- Covers fundamentals and recent developments in the field.
- Includes detailed discussions on group-measure space construction, Krieger factors, and type III_1 hyperfinite factor construction.
- Explores decomposition techniques, duality theory for noncommutative groups, and crossed products.
- Targets students and researchers in mathematics, physics, operator algebras, noncommutative geometry, and free probability.
AI-generated from the title and abstract; the full text is not read.
Abstract
The first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by Ş.V. Strătilă and L. Zsidó) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and researchers interested in operator algebras, noncommutative geometry and free probability, this revised edition covers the fundamentals and latest developments in the field of operator algebras. It discusses the group-measure space construction, Krieger factors, infinite tensor products of factors of type I (ITPFI factors) and construction of the type III_1 hyperfinite factor. It also studies the techniques necessary for continuous and discrete decomposition, duality theory for noncommutative groups, discrete decomposition of Connes, and Ocneanu's result on the actions of amenable groups. It contains a detailed consideration of groups of automorphisms and their spectral theory, and the theory of crossed products.
The authors' abstract, as published at the source. Edinburgh University Press eBooks, 2020 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics