Related papers: Distal actions and ergodic actions on compact grou…

We prove that orbit equivalence of measure preserving ergodic a.e. free actions of a countable group with the relative property (T) is a complete analytic equivalence relation.

We extend some properties of random walks on hyperbolic groups to random walks on convergence groups. In particular we prove that if a convergence group $G$ acts on a compact metrizable space $M$ with the convergence property then we can…

The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among others the method is used to give…

The assignment of local observables in the vacuum sector, fulfilling the standard axioms of local quantum theory, is known to determine uniquely a compact group G of gauge transformations of the first kind together with a central involutive…

This article initiates a geometric study of the automorphism groups of general graph products of groups, and investigates the algebraic and geometric structure of automorphism groups of cyclic product of groups. For a cyclic product of at…

We study meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric…

We construct locally compact groups with no non-trivial Invariant Random Subgroups and no non-trivial Uniformly Recurrent Subgroups.

Reciprocality in Kirchberg algebras with finitely generated K-groups is regarded as a K-theoretic duality through K-groups and strong extension groups. We will prove that the reciprocal Kirchberg algebra has a universal property with…

Let $G$ be a finite group acting effectively on the complex affine plane. If the $G$-action commutes with an \'etale endomorphism $f$ of the affine plane and the order of $G$ is even then the endomorphism $f$ is an automorphism.

We describe the full automorphism group of the directed reduced power graph and the undirected reduced power graph of a finite group. We compute the full automorphism groups of these graphs of several classes of finite groups. Also, we…

In this paper, we show local smooth rigidity for higher rank ergodic nilpotent action by toral automorphisms and prove the existence of such action on any torus TN for any even N ? 6. We also give examples of smooth rigidity of actions…

The paper contains a description of a connection between diagonal actions and certain KMS weights on groupoid $C^{*}$-algebras. It furthermore contains the realization of a graph $C^{*}$-algebra of a countable graph as the groupoid…

We show that in the neighborhood of each ``finite type'' singular orbit of a real analytic integrable dynamical system (hamiltonian or not) there is a real analytic torus action which preserves the system and which is transitive on this…

An automorphism $\alpha$ of a group $G$ is called a commuting automorphism if each element $x$ in $G$ commutes with its image $\alpha(x)$ under $\alpha$. Let $A(G)$ denote the set of all commuting automorphisms of $G$. Rai [Proc. Japan…

An algebraic $Z^{d}$-action is an action of $Z^{d}$ on a compact abelian group $X$ by automorphisms of $X$. We prove that for $d \ge 8$, there exist mixing zero entropy algebraic $Z^{d}$-actions which do not exhibit isomorphism rigidity…

We introduce the notion of graphical discreteness to group theory. A finitely generated group is graphically discrete if whenever it acts geometrically on a locally finite graph, the automorphism group of the graph is compact-by-discrete.…

A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…

In this paper, we discuss certain types of conformal/anticonformal actions of the generalized quasi-dihedral group $G_{n}$ of order $8n$, for $n\geq 2$, on closed Riemann surfaces, pseudo-real Riemann surfaces and compact Klein surfaces,…

We study equivariant morphisms from zero dimensional schemes to varieties and show that, under suitable assumptions, all such morphisms factor via a canonical one. We relate the above to Algebraic Representations of Ergodic Actions.

Let $K$ be a compact connected Lie group acting unitarily on a finite-dimensional complex vector space $V$. One calls this a {\em multiplicity-free} action whenever the $K$-isotypic components of $\C[V]$ are $K$-irreducible. We have shown…