38 problems

Let $X$ be a locally compact space and let $Gamma$ act on $X$, with $C_0(X)\rtimes\Gamma$ the associated crossed-product $C^*$-algebra. Assume the action is amenable and second cou…

Coaction duality conjectures. Every coaction satisfies $E$-crossed-product duality for some $E$, and the dual coaction on every $E$-crossed product $B\rtimes_{\alpha,E}G$ satisfies…

Let $A$ be an infinite-dimensional simple unital C-algebra, let $G$ be a finite group, and let $\alpha \colon G \to \operatorname{Aut}(A)$ be an action with the tracial Rokhlin pro…

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

Let $d$ be a positive integer, let $X$ be the Cantor set, and let $\mathbf{Z}^d$ act freely and minimally on $X$. An AT algebra is an algebra isomorphic to a direct limit … of C-al…

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…

An extended phase space is a Poisson manifold functorially associated with a Poisson covariant system, and it has the structure of a classical principal bundle. A crossed product i…

Let $G$ be a countable amenable group acting freely and minimally on the Cantor set $K$. The associated crossed product $C^*$-algebra is the $C^*$-algebra $C(K)\rtimes G$. Classifi…

Let $A$ be a simple, separable, unital, nuclear, $cmathcal{Z}$-stable $C^*$-algebra, let $G$ be a countable, discrete, amenable group, and let…

Strong 1-boundedness conjecture. The von Neumann algebra $M_{1}$ is strongly $1$-bounded.

Let $X$ be a compact space and let ${\mathbb Z}\curvearrowright X$ be a free minimal action with mean dimension zero. The associated crossed product is $\mathcal Z$-stable. Phillip…

Let $G\curvearrowright_{\alpha}(X,\mathcal{R})$ be an automorphism system. The canonical cocycle induces a coaction $\delta_{\alpha}$ on $C_r^*(\mathcal{R}\rtimes_{\alpha}G)$, and…

Amenability–exactness conjecture. The following conditions are equivalent:

Let $X$ be a compact metric space and let $h$ be a minimal homeomorphism of $X$. Denote by $C^*({\mathbb Z},X,h)$ the crossed product associated to the induced action of…

Let $A$ be a Fréchet–Arens–Michael algebra, not necessarily unital, with a smooth $m$-tempered action $[...$]}]} 金尊 天天中彩票网站?interrupt... 在天天中彩票? Nope. Need valid JSON exact. Need s…

Lifting conjecture. Every approximately inner derivation in $B$ can be lifted to an approximately inner derivation in $A$.

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…

Let $X$ be an infinite, compact, metrizable space, and let $\alpha\colon X\to X$ be a minimal homeomorphism. Set … Then $A$ is a separable, unital, simple, non-elementary, nuclear…

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…

Duality conjecture. These dualities should also hold for the noncommutative smooth orbifold $\mathcal A_\theta \rtimes \Gamma$ under similar restrictions on $\theta$. This extends…

Standing conjecture. Unitary equivalence of the corresponding correspondences is necessary for the existence of an isomorphism between the relative full crossed products.