A duality for Moore groups

On continuous duality for Moore groups

In this paper we correct the errors of Yu.~N.~Kuznetsova's paper on the continuous duality for Moore groups.

半有限von Neumann代数上遍历群作用的Duflo-Moore定理

A Duflo-Moore theorem for ergodic group actions on semifinite von Neumann algebras

本文推广了Duflo-Moore正交关系到半有限von Neumann代数上保持迹的遍历群作用，并得到了卷积不等式，推广了局部紧群上的Young不等式和Werner量子调和分析中的算子-算子卷积不等式。

The Howe-Moore property for real and p-adic groups

We consider in this paper a relative version of the Howe-Moore Property, about vanishing at infinity of coefficients of unitary representations. We characterize this property in terms of ergodic measure-preserving actions. We also characterize, for linear Lie groups or p-adic Lie groups, the pairs with the relative Howe-Moore Property with respect to a closed, normal subgroup. This involves, in one direction, structural results on locally compact groups all of whose proper closed characteristic subgroups are compact, and, in the other direction, some results about the vanishing at infinity of …

The universal group of Burger--Mozes and the Howe--Moore property

By constructing a new unitary representation we prove the universal group $U(F)^+$ of Burger--Mozes does not have the Howe--Moore property when $F$ is primitive but not $2$-transitive. It is well known $U(F)^+$ does have this property when $F$ is $2$-transitive. Along the way, we give a characterization of the universal group, when $F$ is primitive, to have the Howe--Moore property, and also prove $U(F)^+$ has the relative Howe--Moore property. These two results are a consequence of a strengthening of Mautner's phenomenon for locally compact groups acting on d-regular trees and having Tits' in…

An Explicit Duality for Finite Groups

Using a ``3 by 3 matrix trick'' we previously showed that multiplication in a C*-algebra A, an algebraic structure, is determined by the geometry of the C*-algebra of the 3 by 3 matrices with entries from A. As an application of this algebra-geometry duality we now construct an order theoretic based duality theory for all groups which are either locally compact abelian or finite. This construction generalizes the van Kampen--Pontriagin duality for locally compact abelian groups.

Non-Archimedean Duality: Algebras, Groups, and Multipliers

We develop a duality theory for multiplier Banach-Hopf algebras over a non-Archimedean field K. As examples, we consider algebras corresponding to discrete groups and zero-dimensional locally compact groups with K-valued Haar measure, as well as algebras of operators generated by regular representations of discrete groups.