16 problems

Let $(A,G,\alpha)$ be a separable dynamical system, where $A$ is a $C^*$-algebra, $G$ is a locally compact group, and $\alpha$ is an action of $G$ on $A$. The system satisfies the…

Let $M$ be a connected compact smooth manifold with $\dim(M)>0$, and let $h\colon M\to M$ be a uniquely ergodic minimal diffeomorphism. Let…

Let $M$ be a separable II$_1$ factor. Let $G$ be a countably infinite group, let $(B,\tau)$ be a tracial von Neumann algebra, and let $(\sigma,c)$ be a trace-preserving cocycle act…

Amenability–exactness conjecture. The following conditions are equivalent:

Existence conjecture. Two $C^*$-algebras playing the roles of $\mathscr{SC}(U)\rtimes U$ and $\mathscr{SC}(U)\rtimes_\tau U$ can be defined, namely…

Sierakowski's conjecture. If the action of $\Gamma$ on $\widehat{A}$ is essentially free, then $A$ separates the ideals of $A\rtimes_r\Gamma$.

Amenability necessity conjecture. Under these assumptions, the action $\theta$ is amenable. This conjecture would show that amenability is necessary for the transference results co…

Let $\mathcal A_\theta^{alg}$ be the algebraic noncommutative torus and let $\Gamma$ be one of the cyclic groups $\mathbb Z_3$, $\mathbb Z_4$, or $\mathbb Z_6$. The group…

Let $\theta\notin\mathbb Q$, let $\mathcal A_\theta$ be the algebraic irrational rotational algebra, and let $\mathcal A_\theta\rtimes\mathbb Z_2$ denote its crossed product by the…

Let $\mathcal A_\theta^{alg} \rtimes \mathbb Z_2$ be the algebraic noncommutative toroidal orbifold, and let $1,p^\theta,q_0^\theta,q_1^\theta,r^\theta$ be the five projections con…

Let $(X,h)$ be a minimal dynamical system, and assume that $(X,h)$ has the dynamic comparison property. Write $C^{*}({\mathbb Z},X,h)$ for the transformation group $C^{*}$-algebra…

Let $(B,\alpha)$ be an action of a locally compact group $G$ on a $C^*$-algebra $B$, and let $B\rtimes_{\alpha,E}G$ be its $E$-crossed product. Denote by $\hat\alpha_E$ the dual co…

Let $(A,\delta)$ be a coaction of a locally compact group $G$. Say that $(A,\delta)$ satisfies $E$-crossed-product duality when … where $K_\delta$ is the kernel ideal of the Kataya…

The crossed-product factorization conjecture. For any Orlicz function $\psi$,

Let $(A,G)$ be a C-dynamical system with $G$ discrete. The action of $G$ on the spectrum $\widehat{A}$ is called essentially free if, for every closed invariant subset…

The integer-operator conjecture for group-measure-space rings. Every normal operator in this subring is an integer operator. This is the group-measure-space analogue of the conject…