Related papers: Peripheral Poisson Boundary

The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the…

The Poisson boundary of a group G with a probability measure \mu is the space of ergodic components of the time shift in the path space of the associated random walk. Via a generalization of the classical Poisson formula it gives an…

The purpose of this paper is two-fold: firstly, we give a characterization on the level of non-unital operator systems for when the zero map is a boundary representation. As a consequence, we show that a non-unital operator system arising…

We clarify the relation between noncommutative Poisson boundaries and Furstenberg-Hamana boundaries of quantum groups. Specifically, given a compact quantum group $G$, we show that in many cases where the Poisson boundary of the dual…

First, we review the notion of a Poisson structure on a noncommutative algebra due to Block-Getzler and Xu and introduce a notion of a Hamiltonian vector field on a noncommutative Poisson algebra. Then we describe a Poisson structure on a…

Noncommutative or `quantum' differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics) but also differential forms, bundles and…

We formulate Yang-Mills theory in terms of the large-N limit, viewed as a classical limit, of gauge-invariant dynamical variables, which are closely related to Wilson loops, via deformation quantization. We obtain a Poisson algebra of these…

This short note aims to give an insight to Arveson's boundary theorem by means of non-commutative Poisson boundaries and its applications.

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map)…

Let $X$ be a finite connected graph, each of whose vertices has degree at least three. The fundamental group $\Gamma$ of $X$ is a free group and acts on the universal covering tree $\Delta$ and on its boundary $\partial \Delta$, endowed…

Superimposed D-branes have matrix-valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics…

For a locally compact quantum group $\mathbb{G}$, consider the convolution action of a quantum probability measure $\mu$ on $L_\infty(\mathbb{G})$. As shown by Junge--Neufang--Ruan, this action has a natural extension to a Markov map on…

Let S be an operator system -- a self-adjoint linear subspace of a unital C*-algebra A such that contains 1 and A=C*(S) is generated by S. A boundary representation for S is an irreducible representation \pi of C*(S) on a Hilbert space with…

In this paper we study associative algebras with a Poisson algebra structure on the center acting by derivations on the rest of the algebra. These structures, which we call Poisson fibred algebras, appear in the study of quantum groups at…

It is shown that the Poisson bracket with boundary terms recently proposed by Bering (hep-th/9806249) can be deduced from the Poisson bracket proposed by the present author (hep-th/9305133) if one omits terms free of Euler-Lagrange…

In this paper we answer a question of Kaimanovich by characterizing (jointly) bi-harmonic functions on countable, discrete groups with respect to a symmetric, generating measure. We also study the peripheral Poisson boundary of $L(\G)$ with…

In a number of recent papers, the idea of generalized boundaries has found use in fractal and in multiresolution analysis; many of the papers having a focus on specific examples. Parallel with this new insight, and motivated by quantum…

We introduce the notion of Zimmer amenability for actions of discrete quantum groups on von Neumann algebras. We prove generalizations of several fundamental results of the theory in the noncommutative case. In particular, we give a…

The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which…

We compute the Poisson boundary of locally discrete groups of diffeomorphisms of the circle.