Lifting Commutation Relations in Cuntz Algebras

Bruce Blackadar

*(University of Nevada, Reno)*

9:30 am to 10:20 am, June 5th, 2015 Science Building A1414

__Abstract:__

We examine splitting of the quotient map from the full free product
$A * B$, or the unital free product $A *_{\mathbb{C}} B$, to the (maximal) tensor product $A \otimes B$, for unital $C^*$-algebras $A$ and $B$. Such a splitting is very rare, but we show
there is one if $A$ and $B$ are both the Cuntz algebra $\mathcal{O}_2$ or $\mathcal{O}_{\infty}$, and in a few
other cases. The splitting is not explicit (and in principle probably cannot be).
We also describe several $K$-theoretic obstructions to a splitting.

__About the speaker:__

Bruce Blackadar is a professor at University of Nevada, Reno.

__Attachments:__