Operator Algebras and Applications: The Abel Symposium 2015

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Toke M. Carlsen, Nadia S. Larsen, Sergey Neshveyev, Christian Skau
Springer, Jul 30, 2016 - Mathematics - 348 pages

Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject.

The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis.

This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.

 

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Contents

CTensor Categories and Subfactors for Totally Disconnected Groups
1
Decomposable Approximations Revisited
44
Exotic Crossed Products
67
On Hong and Szymańskis Description of the PrimitiveIdeal Space of a Graph Algebra
115
Commutator Inequalities via Schur Products
133
CAlgebras Associated with Algebraic Actions
150
A New Look at CSimplicity and the Unique Trace Property of a Group
167
Equilibrium States on Graph Algebras
177
Semigroup CAlgebras
190
Topological Full Groups of Étale Groupoids
203
Towards a Classification of Compact Quantum Groups of Lie Type
231
A Summary
265
On the Positive Eigenvalues and Eigenvectors of a Nonnegative Matrix
276
A Selective Survey
303
QDQ vs UCT
327
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