Lifting Commutation Relations in Cuntz Algebras

Abstract

We examine splitting of the quotient map from the full free product $A\ast B$, or the unital free product $A{\ast }_{\mathbb{C}}B$, 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 $O_2$ or $O_{\infty }$, and in a few other cases. The splitting is not explicit (and in principle probably cannot be). We also describe severe $K$-theoretic obstructions to a splitting.

15 pages; revised, corrections and additions

References in corpus (1)

• Semiprojectivity for Kirchberg algebras

Cited by in corpus (1)

• Semiprojectivity for Kirchberg algebras