Central sequence algebras and their Cuntz semigroups
Aaron Tikuisis (University of Aberdeen)
Tuesday 25th February, 2014 16:00-17:00 Maths 416
The notion of approximately central sequences has repeatedly proved to be crucial in the study of operator algebras - both von Neumann algebras and C*-algebras, although this talk will be only concerned with the latter. This notion is neatly packed into an object called the central sequence algebra. Various properties of a C*-algebra can be read off simply from the Cuntz semigroup of its central sequence algebra (Jiang-Su stability comes most readily to mind here). This has prompted a more detailed analysis of the finer structure of such Cuntz semigroups. Much of this analysis concerns the embedding of the central sequence algebra into the sequence algebra, and the structure of the induced map on Cuntz semigroups (note that the sequence algebra, and its Cuntz semigroup, are much easier objects to understand). It is interesting to ask: To which extent is this map an order embedding? How close is this map to being surjective? I will make these questions more precise in the talk. This project is still in its infancy, and I will report on answers to these questions in the case of simple AF algebras. It is joint work with I. Farah and L. Robert. The University of Aberdeen is a charity registered in Scotland, No SC013683.