Related papers: Isomorphism rigidity of commuting automorphisms

Given a countable group $G$ and two subshifts $X$ and $Y$ over $G$, a continuous, shift-commuting map $\phi : X \to Y$ is called a homomorphism. Our main result states that if every finitely generated subgroup of $G$ has polynomial growth,…

We prove that the restriction of a probability measure invariant under a nonhyperbolic, ergodic and totally irreducible automorphism of a compact connected abelian group to the leaves of the central foliation is severely restricted. We also…

Let $A$ be a group acting by automorphisms on the group $G.$ \textit{The commuting graph $\Gamma(G,A)$ of $A$-orbits} of this action is the simple graph with vertex set $\{x^{A} : 1\ne x \in G \}$, the set of all $A$-orbits on $G\setminus…

We prove that if a measure distal action $\alpha$ of a countable group $\Gamma$ is weakly contained in a strongly ergodic probability measure preserving action $\beta$ of $\Gamma$, then $\alpha$ is a factor of $\beta$. In particular, this…

We study the rigidity properties of a class of algebraic Z^3-actions with entropy rank two. For this class, conditions are found which force an invariant measure to be the Haar measure on an affine subset. This is applied to show…

We determine the geometric structure of a minimal projective threefold having two `independent and commutative' automorphisms of positive topological entropy, and generalize this result to higher-dimensional smooth minimal pairs (X, G). As…

We prove that a unital completely positive map between finite-dimensional C*-algebras is a homomorphism if and only if it is completely entropy-nonincreasing, where the relevant notion of entropy is a variant of von Neumann entropy. This…

Let $K$ be a compact metrizable group and $\Ga$ be a group of automorphisms of $K$. We first show that each $\ap \in \Ga$ is distal on $K$ implies $\Ga$ itself is distal on $K$, a local to global correspondence provided $\Ga$ is a…

If $X$ is a locally compact space which admits commuting free and proper actions of locally compact groups $G$ and $H$, then the Brauer groups $\Br_H(G/X)$ and $\Br_G(X/H)$ are naturally isomorphic.

The action of a finite group $G$ on a subshift of finite type $X$ is called free, if every point has trivial stabilizer, and it is called inert, if the induced action on the dimension group of $X$ is trivial. We show that any two free inert…

Let S be a finite generating set of a torsion-free, nilpotent group G. We show that every automorphism of the Cayley graph Cay(G;S) is affine. (That is, every automorphism of the graph is obtained by composing a group automorphism with…

We show that the automorphism group of every zero entropy infinite shift admits a "drift" homomorphism to $(\mathbb{R},+)$ that maps the shift map to 1. This homomorphism arises as the expectation, under an invariant measure, of a cocycle…

The superextension $\lambda(X)$ of a set $X$ consists of all maximal linked families on $X$. Any associative binary operation $*: X\times X \to X$ can be extended to an associative binary operation $*:…

Let $G$, $H$ be groups and $\kappa$ be a cardinal. A bijection $f:G\to H$ is caled on asymorphism if, for any $X\in[G]^{<\kappa}$, $Y\in[H]^{<\kappa}$, there exist $X'\in[G]^{<\kappa}$, $Y'\in[H]^{<\kappa}$ such that for all $x\in G$ and…

Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…

We give examples of principal algebraic actions of the noncommutative free group $F$ of rank two, as well as other groups, by automorphisms of a connected compact abelian group for which there is an explicit measurable isomorphism to a…

We study pairs of non-constant maps between two integral schemes of finite type over two (possibly different) fields of positive characteristic. When the target is quasi-affine, Tamagawa showed that the two maps are equal up to a power of…

A group G acts infinitely transitively on a set Y if for every positive integer m, its action is m-transitive on Y. Given a real affine algebraic variety Y of dimension greater than or equal to two, we show that, under a mild restriction,…

Let $\Gamma$ be a sofic group with a copy of $\mathbb{Z}$ in its center. We construct an uncountable family of pairwise nonisomorphic measure-preserving $\Gamma$ actions with completely positive entropy, none of which is a factor of a…

In this paper, we study a natural class of groups that act as affine transformations of $\mathbb T^N$. We investigate whether these solvable, "abelian-by-cyclic," groups can act smoothly and nonaffinely on $\mathbb T^N$ while remaining…