For more information about this meeting, contact Nigel Higson, Mari Royer, John Roe.
|Title:||The generator problem for C*-algebras|
|Seminar:||Noncommutative Geometry Seminar|
|Speaker:||Hannes Thiel, University of Copenhagen|
|The generator problem asks to determine for a given C*-algebra the minimal number of generators, i.e., elements that are not contained in a proper C*-subalgebra. It is conjectured that every separable, simple C*-algebra is generated by a single element. The generator problem was originally asked for von Neumann algebras, and Kadison included it as number 14 of his famous list of 20 “Problems on von Neumann algebras”. The general problem is still open, most notably for the free group factors.
With Wilhelm Winter, we proved that every a unital, separable C*-algebra is generated by a single element if it tensorially absorbs the Jiang-Su algebra. This generalized most previous results about the generator problem for C*-algebra.
In a different approach to the generator problem, we define a notion of `generator rank', in analogy to the real rank. Instead of asking if a certain C*-algebra A is generated by k elements, the generator rank records whether the generating k-tuples of A are dense. It turns out that this invariant has good permanence properties, for instance it passes to inductive limits. It follows that every AF-algebra is singly generated, and even more the set of generators is generic (a dense G_delta-set).|
Room Reservation Information
|Date:||04 / 24 / 2014|
|Time:||02:30pm - 03:30pm|