Lifting Commutation Relations in Cuntz Algebras

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.