Operator Algebras and Applications: The Abel Symposium 2015

✍ Scribed by Toke M. Carlsen, Nadia S. Larsen, Sergey Neshveyev, Christian Skau (eds.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 345
• Series: Abel Symposia 12
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-x
C∗-Tensor Categories and Subfactors for Totally Disconnected Groups....Pages 1-43
Decomposable Approximations Revisited....Pages 45-59
Exotic Crossed Products....Pages 61-108
On Hong and Szymański’s Description of the Primitive-Ideal Space of a Graph Algebra....Pages 109-126
Commutator Inequalities via Schur Products....Pages 127-143
C∗-Algebras Associated with Algebraic Actions....Pages 145-159
A New Look at C∗-Simplicity and the Unique Trace Property of a Group....Pages 161-170
Equilibrium States on Graph Algebras....Pages 171-183
Semigroup C∗-Algebras....Pages 185-196
Topological Full Groups of Étale Groupoids....Pages 197-224
Towards a Classification of Compact Quantum Groups of Lie Type....Pages 225-257
A Homology Theory for Smale Spaces: A Summary....Pages 259-269
On the Positive Eigenvalues and Eigenvectors of a Non-negative Matrix....Pages 271-296
Classification of Graph Algebras: A Selective Survey....Pages 297-319
QDQ vs. UCT....Pages 321-342

✦ Subjects

Functional Analysis;Dynamical Systems and Ergodic Theory;K-Theory;Mathematical Physics