Anomalous symmetries of classifiable C*-algebras - Girón Pacheco, S (2023)
This thesis studies the existence and uniqueness of $G$-kernels on those C$^*$-algebras classified by the Elliott programme. We develop two obstructions to the possible $H^3$ invariants of a $G$-kernel. These obstructions arise from studying the unitary algebraic $K_1$ group and the topological $K_0$ group of a C$^*$-algebra. As a consequence of these obstructions, we show that any $G$-kernel on the Jiang-Su algebra has trivial $H^3$ invariant. Similarly, for finite groups $G$, any $G$-kernel on the Cuntz algebra $\mathcal{O}_∞$ must have trivial $H^3$ invariant.