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Thursday, November 14, 2019 — 12:00 PM EST

Dan Ursu, Pure Math Department, University of Waterloo

"Relative C*-Simplicity"

Groups are good for one thing and that's acting on things. We can consider the action of a group G on a C*-algebra A, and just like for the semidirect product of two groups, we can embed G and A into a larger C*-algebra where the action is inner. This forms what's called a crossed product. A recent result of Amrutam gives a sufficient condition for all C*-subalgebras of a crossed product that contain G to also themselves be crossed products with G. Namely, this is true if the kernel of the action of G on A is what he calls plump.

Plumpness is a relative version of something called Power's averaging property, which is known to being equivalent to the reduced C*-algebra of G being simple (i.e. G is C*-simple). With this in mind, and with the intention of coming up with a better name than plump, we come up with the notion of a relatively C*-simple subgroup of G, and it is possible to show that these two notions are equivalent, along with several other characterizations.

In this talk, I will build up all of the necessary prerequisites, and give a brief overview of the equivalences mentioned earlier. Finally, with this, I will prove some easy examples of relatively C*-simple subgroups.

MC 5403

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