7 problems

Proper-action characterization. The following are equivalent:

Let $A$ be a locally compact quantum group (LCQG). A finite-dimensional corepresentation of $A$ is admissible if both the corepresentation $V$ and its transpose $V^t$ are invertibl…

Let $\mathbb{G}$ be a locally compact quantum group. Suppose that $C_0(\mathbb{G})$ is nuclear and that there exists a state $\rho\in C_0(\mathbb{G})^*$ such that … for every…

Amenability–nuclearity equivalence conjecture. Condition prettyref{enu:amennuc1b} is equivalent either to condition prettyref{enu:amennuc1a} or to condition prettyref{enu:amennuc1c…

Let $\mathbb{G}$ be a locally compact quantum group. In the discussion of converting a result for $L^1(\mathbb{G})$ into the corresponding result for $L^2(\mathbb{G})$, consider a…

Let $\mathbb{G}$ be a locally compact quantum group and let $\hat{\mathbb{G}}$ be its dual. The associated convolution algebras are $L^1(\mathbb{G})$ and $L^1(\hat{\mathbb{G}})$. D…

Let $\mathbb{G}$ be a discrete quantum group, with dual compact quantum group $\hat{\mathbb{G}}$ and von Neumann algebra $L^{\infty}(\hat{\mathbb{G}})$. The algebra…