Compact groups with a set of positive Haar measure satisfying a nilpotent law

Haar Measure for Compact Right Topological Groups

Compact right topological groups arise in topological dynamics and in other settings. Following H. Furstenberg's seminal work on distal flows, R. Ellis and I. Namioka have shown that the compact right topological groups of dynamical type always admit a probability measure invariant under the continuous left translations; however, this invariance property is insufficient to identify a unique pro...

The Characteristic Polynomial on Compact Groups with Haar Measure : Some Equalities in Law

Abstract. This note presents some equalities in law for ZN := det(Id− G), where G is an element of a subgroup of the set of unitary matrices of size N , endowed with its unique probability Haar measure. Indeed, under some general conditions, ZN can be decomposed as a product of independent random variables, whose laws are explicitly known. Our results can be obtained in two ways : either by a r...

A Property of the Haar Measure of Some Special LCA Groups

The Euclidean group (Rn,+) where (n?N, plays a key role in harmonic analysis. If we consider the Lebesgue measure ()nd?xR as the Haar measure of this group then 12(2)()nd?x=d?RR. In this article we look for LCA groups K, whose Haar measures have a similar property. In fact we will show that for some LCA groups K with the Haar measure K?, there exists a constant such that 0KC>()(2)KKK?A=C?A for ...

The Haar measure on some locally compact quantum groups

A locally compact quantum group is a pair (A,Φ) of a C-algebra A and a -homomorphism Φ from A to the multiplier algebra M(A ⊗ A) of the minimal C-tensor product A ⊗ A satisfying certain assumptions (see [K-V1] and [K-V2]). One of the assumptions is the existence of the Haar weights. These are densely defined, lower semi-continuous faithful KMS-weights satisfying the correct invariance propertie...

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup