Related papers: On solid ergodicity for Gaussian actions

The theorems of M. Ratner, describing the finite ergodic invariant measures and the orbit closures for unipotent flows on homogeneous spaces of Lie groups, are extended for actions of subgroups generated by unipotent elements. More…

Let $G$ be a noncompact semisimple algebraic group with trivial center, $S < G$ a maximal split torus, $H < G$ the centralizer of $S$ in $G$ and $\Gamma < G$ an irreducible lattice. Consider the group measure space von Neumann algebra…

We introduce the notion of proper proximality for finite von Neumann algebras, which naturally extends the notion of proper proximality for groups. Apart from the group von Neumann algebras of properly proximal groups, we provide a number…

We introduce a framework allowing for key aspects of deformation/rigidity theory to be used in the study of continuous model theory of II$_1$ factors. Using this framework, we solve several well-known open problems in the area. For example,…

In this paper, we show that the Givental group action on genus zero cohomological field theories, also known as formal Frobenius manifolds or hypercommutative algebras, naturally arises in the deformation theory of Batalin--Vilkovisky…

We study actions of countable discrete groups which are amenable in the sense that there exists a mean on X which is invariant under the action of G. Assuming that G is nonamenable, we obtain structural results for the stabilizer subgroups…

Given a $\mathbb Z^r$-action $\alpha$ on a nilmanifold $X$ by automorphisms and an ergodic $\alpha$-invariant probability measure $\mu$, we show that $\mu$ is the uniform measure on $X$, unless modulo finite index modification, one of 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…

We first note that, at least in perturbation theory, there is a well-defined (subject to regularization) Lorentzian definition of the quantum effective action in both flat and curved space including (perturbative) gravity. The advantage of…

Let $G$ be a connected semisimple real algebraic group. The class of transverse subgroups of $G$ includes all discrete subgroups of rank one Lie groups and any subgroups of Anosov or relative Anosov subgroups. Given a transverse subgroup…

We explore a duality between von-Neumann's mean ergodic theorem in von-Neumann algebra and Birkhoff's mean ergodic theorem in the pre-dual Banach space of von-Neumann algebras. Besides improving known mean ergodic theorems on von-Neumann…

Dan Rudolph showed that for an amenable group $\Gamma$, the generic measure-preserving action of $\Gamma$ on a Lebesgue space has zero entropy. Here this is extended to nonamenable groups. In fact, the proof shows that every action is a…

We investigate translation actions of countable dense subgroups of non-unimodular locally compact second countable (lcsc) groups. Using left-right actions, we show that the left translation action $\Gamma \curvearrowright G$ given by a…

Local mean and individual (with respect to almost uniform convergence in Egorov's sense) ergodic theorems are established for actions of the semigroup $\mathbb R_+^d$ in symmetric spaces of measurable operators associated with a semifinite…

Let $\delta$ be a nondegenerate coaction of G on a C*-algebra B, and let H be a closed subgroup of G. The dual action of H on $B\times_\delta G$ is proper and saturated in the sense of Rieffel, and the generalised fixed-point algebra is the…

Let $G$ be a connected semisimple real algebraic group and $\Gamma$ a Zariski dense Anosov subgroup of $G$ with respect to a minimal parabolic subgroup $P$. Let $N$ be the maximal horospherical subgroup of $G$ given by the unipotent radical…

We prove some finiteness results for discrete isometry groups $\Gamma$ of uniformly packed CAT$(0)$-spaces $X$ with uniformly bounded codiameter (up to group isomorphism), and for CAT$(0)$-orbispaces $M = \Gamma \backslash X$ (up to…

We first introduce an invariant index for G-equivariant elliptic differential operators on a locally compact manifold M admitting a proper cocompact action of a locally compact group G. It generalizes the Kawasaki index for orbifolds to the…

Lie-Poisson electrodynamics describes a semiclassical approximation of noncommutative $U(1)$ gauge theories with Lie-algebra-type noncommutativities. We obtain a gauge-invariant local classical action with the correct commutative limit for…

We establish that particular quotients of the non-commutative Hardy algebras carry ergodic actions of convergent discrete subgroups of the group $\operatorname*{SU}(n,1)$ of automorphisms of the unit ball in $\mathbb{C}% ^{n}$. To do so, we…