Add to ORKGWe investigate almost minimal actions of abelian groups and their crossed products. As an application, given multiplicatively independent integers $p$ and $q$, we show that Furstenberg's $\times p,\times q$ conjecture holds if and only if the canonical trace is the only faithful extreme tracial state on the $C^*$-algebra of the group $\mathbb{Z}[\frac{1}{pq}]\rtimes\mathbb{Z}^2$. We also compute the primitive ideal space and K-theory of $C^*(\mathbb{Z}[\frac{1}{pq}]\rtimes\mathbb{Z}^2)$.Comment: 12 pages. Fixed a gap in the proof of Theorem 3.10. Accepted in the Canadian Mathematical Bulleti
We show that the principal algebraic actions of countably infinite groups associated to lopsided ele...
Given a topologically free action of a countable group $G$ on a compact metric space $X$, there is a...
We describe a weak tracial analog of approximate representability under the name "weak tracial appro...
The Mautner groups are the 5-dimensional solvable Lie groups that have non-type-I factor representat...
In this work, we will explore the relation between topological dynamical systems and their reduced c...
We introduce and study the notions of boundary actions and of the Furstenberg boundary of a discrete...
Let $\mathbb{N}^{2}$ be the positive cone of the abelian lattice-ordered group $\mathbb{Z}^{2}$. Let...
We define a "tracial" analog of the Rokhlin property for actions of second countable compact groups ...
A. Borisov classified into finitely many series the set of isomorphism classes of germs of toric $\Q...
Let $X \subset \mathbb{C}^n$ be an algebraic variety, and let $\Lambda \subset \mathbb{C}^n$ be a di...
Given a commensurated subgroup $\Lambda$ of a group $\Gamma$, we completely characterize when the in...
We generalize the well known $C^*$-algebraic result of Kawamura-Tomiyama and Archbold-Spielberg for ...
Given a second-countable, locally compact group $G$, we consider equivariantly $\mathcal{O}_2$-stabl...
Let $B$ be a separable $C^*$-algebra, let $\Gamma$ be a discrete countable group, let $\alpha: \Gamm...
For a smooth projective variety $X$ over a number field $k$ a conjecture of Bloch and Beilinson pred...
We show that the principal algebraic actions of countably infinite groups associated to lopsided ele...
Given a topologically free action of a countable group $G$ on a compact metric space $X$, there is a...
We describe a weak tracial analog of approximate representability under the name "weak tracial appro...
The Mautner groups are the 5-dimensional solvable Lie groups that have non-type-I factor representat...
In this work, we will explore the relation between topological dynamical systems and their reduced c...
We introduce and study the notions of boundary actions and of the Furstenberg boundary of a discrete...
Let $\mathbb{N}^{2}$ be the positive cone of the abelian lattice-ordered group $\mathbb{Z}^{2}$. Let...
We define a "tracial" analog of the Rokhlin property for actions of second countable compact groups ...
A. Borisov classified into finitely many series the set of isomorphism classes of germs of toric $\Q...
Let $X \subset \mathbb{C}^n$ be an algebraic variety, and let $\Lambda \subset \mathbb{C}^n$ be a di...
Given a commensurated subgroup $\Lambda$ of a group $\Gamma$, we completely characterize when the in...
We generalize the well known $C^*$-algebraic result of Kawamura-Tomiyama and Archbold-Spielberg for ...
Given a second-countable, locally compact group $G$, we consider equivariantly $\mathcal{O}_2$-stabl...
Let $B$ be a separable $C^*$-algebra, let $\Gamma$ be a discrete countable group, let $\alpha: \Gamm...
For a smooth projective variety $X$ over a number field $k$ a conjecture of Bloch and Beilinson pred...
We show that the principal algebraic actions of countably infinite groups associated to lopsided ele...
Given a topologically free action of a countable group $G$ on a compact metric space $X$, there is a...
We describe a weak tracial analog of approximate representability under the name "weak tracial appro...