Loop group actions on Cuntz algebras and geometric higher twists

Abstract

We consider representations of the Cuntz algebras ${\mathcal{O}}_N$ as constructed by Bratteli-Jorgensen and use these to define a faithful action of the analytic loop group $L_{\text{an}}U(n)$ on ${\mathcal{O}}_N$ for $N\ge n$. This extends to a faithful action on the infinite Cuntz algebra ${\mathcal{O}}_{\infty }$, and we show that this action can be used to explicitly construct ${\mathcal{O}}_{\infty }\otimes \mathcal{K}$-bundles (where $\mathcal{K}$ is the algebra of compact operators) over spaces, which are geometric twists in higher twisted $K$-theory.

Fatal error in the definition of the action. The authors thank R. Conti for pointing this out