Bartosz Kwaśniewski

Invitation to actions of $C^*$-correspondences

The 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.

XXXVI Workshop on Geometric Methods in Physics	2-8.07.2017
VI School on Geometry and Physics	26-30.06.2017

Event sponsored by:
		University of Bialystok