Structure and classification of simple amenable C* algebras

author: Stuart White, Oxford University
published: July 6, 2021,   recorded: July 2021,   views: 1

Related Open Educational Resources

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.


In this talk I will give an overview of recent progress in the structure theory of simple amenable C ∗ -algebras and classification results. C ∗ -algebras are norm closed self-adjoint subalgebras of the bounded operators on a Hilbert space, with examples arising naturally from unitary representations of groups, and topological dynamics. They have a topological flavour, seen through the commutative algebras of continuous functions on locally compact Hausdorff spaces. The classification of C ∗ -algebras has its spiritual origins in the powerful structure and classification theorems for von Neumann algebras of Connes in the ’70s. However, in the topological setting of C ∗ -algebras, higher dimensional phenomena can obstruct classification in general. Progress over the last decade has seen the identification of abstract structural conditions which give the maximal family of algebras which can be classified by K-theory and traces. These conditions now have equivalent formulations of very different natures, which can be used to bring naturally occurring examples within the scope of classification. The talk is based in part on joint works with Castillejos, Carri´on, Evington, Gabe, Schafhauser, Tikuisis, and Winter.

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Write your own review or comment:

make sure you have javascript enabled or clear this field: