Operator Algebras and Applications: The Abel Symposium 2015

Description

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 speci fic 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. 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