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

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.
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