XXXVI Workshop on Geometric Methods in Physics | 2-8.07.2017 |
VI School on Geometry and Physics | 26-30.06.2017 |
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Bartosz KwaśniewskiInvitation to actions of $C^*$-correspondencesThe lectures are planned to be a gentle introduction to the theory of $C^*$-correspondences and their actions on $C^*$-algebras. Amongst the structures that can be unified from this point of view are product systems, Fell bundles and groupoids. A $C^*$-correspondence from a $C^*$-algebra $A$ to a $C^*$-algebra $B$ is a right Hilbert $A$-module equipped with a left action of $B$ by adjointable operators. In the context of $W^*$-algebras the term correspondence was introduced by A. Connes in 1960's. It can be interpreted as a noncommutative graph (relation) between two operator algebras. After the seminal paper by M. Pimsner in 1997, "A class of $C^*$-algebras generalizing both Cuntz-Krieger algebras and crossed products by $\mathbb{Z}$", $C^*$-correspondences became a fundamental tool in the theory of $C^*$-algebras given by relations of dynamic or combinatorial nature. |
Event sponsored by: | |||||
University of Bialystok |