4 problems

Let $B=M_n(\mathbb C)$, and let $\Gamma$ be the convex set of states $\phi$ on $B\otimes B$ whose restrictions to $B\otimes I$ and $I\otimes B$ are the unique tracial states on tho…

Let $C^*(\mathbb{Z}[1/6])$ be regarded as a subalgebra of $C^*(\mathfrak{F}_{2,3})$, let $\operatorname{TSt}(C^*(\mathfrak{F}_{2,3}))$ denote the tracial states, call a state condi…

A topological graph $E$ has a vertex space $E^0$ and an associated $C^*$-algebra equipped with a natural circle-group gauge action. A tracial state on this $C^*$-algebra is gauge-i…

Let $E$ be a free topological graph, and let $C^{*}(E)$ denote its graph $C^{*}$-algebra. A tracial state on $C^{*}(E)$ is a state $\tau:C^{*}(E)\to\mathbb{C}$ satisfying…