Related papers: Poissonian Actions of Polish Groups

We continue the study of Calogero-Moser spaces associated with dihedral groups by investigating in more details the equal parameter case: we obtain explicit equations, some informations about the Poisson bracket, the structure of the Lie…

Let k be a field of positive characteristic p and let G be a finite group. In this paper we study the category TsG of finitely generated commutative k-algebras A on which G acts by algebra automorphisms with surjective trace. If A = k[X],…

We look at group actions on metric spaces, particularly at group actions on geodesic hyperbolic spaces. We classify the types of automorphisms on these spaces and prove several results about the density of the hyperbolic limit set of the…

Symplectic slice theorems elucidate the local structure of symplectic manifolds carrying Hamiltonian actions of compact Lie groups. We generalize these theorems in two natural settings. The first is based on the idea that complex reductive…

We give a geometric description of the Poisson boundaries of certain extensions of free and hyperbolic groups. In particular, we get a full description of the Poisson boundaries of free-by-cyclic groups. We rely upon the description of…

We construct explicitly a class of coboundary Poisson-Lie structures on the group of formal diffeomorphisms of ${\Bbb R}^n$. Equivalently, these give rise to a class of coboundary triangular Lie bialgebra structures on the Lie algebra $W_n$…

The orbit-fixing deformation spaces of $C^\infty$ locally free actions of simply connected Lie groups on closed $C^\infty$ manifolds have been studied by several authors. In this paper we reformulate the deformation space by imitating the…

To an ergodic, essentially free and measure-preserving action of a non-amenable Baumslag-Solitar group on a standard probability space, a flow is associated. The isomorphism class of the flow is shown to be an invariant of such actions of…

Let $X = \left\{P \in [0,1]^{\bf N} : \left(\forall \nu \in {\bf N} \right) \left(P \left(\{\nu \} \right) > 0 \right) \wedge \sum\limits_{\nu = 0}^{\infty} P \left(\{\nu \} \right) = 1 \right\} $ be the Polish space of probability measures…

Suppose that $X$ is a Polish space, $E$ is a countable Borel equivalence relation on $X$, and $\mu$ is an $E$-invariant Borel probability measure on $X$. We consider the circumstances under which for every countable non-abelian free group…

This manuscript is essentially a collection of lecture notes which were given by the first author at the Summer School Wisl-2019, Poland and written down by the second author. As the title suggests, the material covered here includes the…

We introduce the concept of an $\mathrm{L}^{1}$ full group associated with a measure-preserving action of a Polish normed group on a standard probability space. These groups carry a natural Polish group topology induced by an $\mathrm{L}^1$…

We consider conformal actions of simple Lie groups on compact Lorentzian manifolds. Mainly motivated by the Lorentzian version of a conjecture of Lichnerowicz, we establish the alternative: Either the group acts isometrically for some…

We present a comprehensive theory of boundedness properties for Polish groups developed with a main focus on Roelcke precompactness (precompactness of the lower uniformity) and Property (OB) (boundedness of all isometric actions on…

We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.

Sorin Popa initiated the study of Polish groups which are embeddable into the unitary group of a separable finite von Neumann algebra. Such groups are called of finite type. We give necessary and sufficient conditions for Polish groups to…

The Poisson and Martin boundaries for invariant random walks on the dual of the orthogonal quantum groups A_o(F), are identified with higher dimensional Podles spheres that we describe in terms of generators and relations. This provides the…

We extend in a noncommutative setting the individual ergodic theorem of Nevo and Stein concerning measure preserving actions of free groups and averages on spheres $s_{2n}$ of even radius. Here we study state preserving actions of free…

A family of Poisson structures, parametrised by an arbitrary odd periodic function $\phi$, is defined on the space $\cW$ of twisted polygons in $\RR^\nu$. Poisson reductions with respect to two Poisson group actions on $\cW$ are described.…

Extending some results of a joint work with E. Glasner, we continue to study the Polish group $G:=\mathrm{Aut}(\mathbb{Q}_0)$ of all circular order preserving permutations of the rational circle $\mathbb Q_0=\mathbb Q/\mathbb Z$, endowed…