4 problems

Let $(N,M,\alpha,\beta,\Gamma,\mu,T_L,T_R)$ be an adapted measured quantum groupoid, meaning a measured quantum groupoid with the stated adaptedness property, and suppose that $M$…

Let $(N,M,\alpha,\beta,\Gamma,\mu,T_L,T_R)$ be a measured quantum groupoid, and suppose that $M$ is commutative. Let $G$ denote a locally compact groupoid, with unit space…

A locally compact groupoid or quantum groupoid is considered together with convolution products of functions having locally compact support. Conjecture. Similar results to the corr…

Pointwise parametrization conjecture. Every element of $\Phi^{r}_{A(G)}$ is of the form $\alpha_{\gamma}$ for some $\gamma\in\Delta^{r}$, and $\Delta^{r}$ with the topology of poin…