11 problems

Anti-deformation conjecture. Any Woronowicz algebra is a dimension-preserving $R^+$-deformation of a Woronowicz-Kac algebra.

Finiteness conjecture. There are only finitely many Woronowicz algebras having a given $(R^+,list)$ invariant.

Kac type characterization conjecture. If

Let $A$ be a unital $C^*$-algebra with a free coaction $\delta$ of a nontrivial compact quantum group $(H, \Delta)$. Equip the join $A \circledast^{\delta} H$ with the induced free…

Noncommutative Borsuk–Ulam conjecture. There does not exist a $\mathbb{G}$-equivariant $*$-homomorphism

Let $A$ be a unital C-algebra equipped with a free action of a non-trivial compact quantum group $(H,\Delta)$, and let $A\circledast^\delta H$ be the equivariant noncommutative joi…

Let $\mathbb{G}$ be the compact quantum group under consideration, let $\widehat{\mathbb{G}}$ be its set of irreducible representations, and let $\Sigma=\{F_n\}$ be a sequence of f…

Let $G\subset U_N^+$ be a compact quantum group, and let $\widehat{G}$ denote its discrete dual. For each $Q\in U_N$, let $\Gamma_Q$ be the associated discrete quantum group. Polyn…

Let $G\subset U_N^+$ be a compact quantum group. Write $C_{\max}(G)$ and $C_{\min}(G)$ for its maximal and minimal Hopf $C^*$-algebras; $G$ is coamenable when the canonical quotient…

Let $G\subset U_N^+$ be a connected compact quantum group. Its central algebra $C(G)_{central}$ is the norm closure of the linear span of irreducible representation characters. For…

Let $\mathcal{G}$ be a compact quantum group acting on a compact Hausdorff space $X$. For $x\theta X$, let $rm Orb_x$ denote the orbit of $x$, let $rm supp\,\mu_x$ denote the suppo…