Karen Strung

Graph $C^{*}$ -algebras and their applications to quantum spaces

This short course will serve as an introduction to

C^{*}

-algebras through the lens of graph algebras, with an emphasis on their role as noncommutative topological spaces. After a short introduction to the basics of

C^{*}

-algebras, we will show how to construct of

C^{*}

-algebras from directed graphs. Graph

C^{*}

-algebras are a class of examples which are both rich and tractable. In particular, we will see how the combinatorics of the graph can determine key

C^{*}

-algebraic properties such as ideal structure and K-theory.

Building on this foundation, we will explore how certain

C^{*}

-algebras arising in noncommutative geometry, which we think of as algebras of functions on “quantum spaces”, can be realized within this framework, by considering the

C^{*}

-algebras of quantum flag manifolds in the sense of Drinfeld and Jimbo.

Karen Strung

Graph C∗-algebras and their applications to quantum spaces

Graph $C^{*}$ -algebras and their applications to quantum spaces