Related papers: Connected Lie groups and property RD

Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an `evolution operator' exists). Up to now all known smooth Lie groups…

In this work, we will introduce and study the notion of local randomness for compact metric groups. We prove a mixing inequality as well as a product result for locally random groups under an additional dimension condition on the volume of…

We develop the theory of locally analytic representations of compact $p$-adic Lie groups from the perspective of the theory of condensed mathematics of Clausen and Scholze. As an application, we generalise Lazard's isomorphisms between…

To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…

A locally compact group $G$ has the factorization property if the map $$C^*(G)\odot C^*(G)\ni a\otimes b\mapsto \lambda(a)\rho(b)\in\mathcal B(L^2(G))$$ is continuous with respect to the minimal C*-norm. This paper seeks to initiate a…

We classify connected Lie groups which are locally isomorphic to generalized Heisenberg groups. For a given generalized Heisenberg group $N$, there is a one-to-one correspondence between the set of isomorphism classes of connected Lie…

We extend the Delorme-Guichardet characterization of Kazhdan property $T$ groups to $r$-discrete measured groupoids. We give several applications, in particular to stability results of Kazhdan property $T$ and to the study of cocycles…

For a Lie groupoid there is an analytic index morphism which takes values in the $K-$theory of the $C^*$-algebra associated to the groupoid. This is a good invariant but extracting numerical invariants from it, with the existent tools, is…

Relevance of local GL(d,R) Lie group for solving quantum ADM constraints is pointed out. Noncommutative harmonic analysis on $GL(d,R)/O(d)$ provides a natural basis and techniques for calculations. This is summarized. Such a basis is…

We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…

We show that relative Property (T) for the abelianization of a nilpotent normal subgroup implies relative Property (T) for the subgroup itself. This and other results are a consequence of a theorem of independent interest, which states that…

The semidirect product $\mathbb{G}=\mathbb{L}\rtimes \mathbb{K}$ attached to a compact-group action on a connected, simply-connected solvable Lie group has a dense set of compact elements precisely when the $s\in \mathbb{K}$ operating on…

Let $G$ be a (non compact) connected simply connected locally compact second countable Lie group, either abelian or unimodular of type I, and $\rho$ an irreducible unitary representation of $G$. Then, we define the analytic torsion of $G$…

A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for…

We consider bicrossed products obtained by twisting compact semi-direct products by a suitable finite subgroup. Under some restriction, we give a practical criterion for the discrete dual of such bicrossed products to have the rapid decay…

We consider a class of non-locally compact groups on which one may define a left-invariant, finitely additive measure taking values in some finitely generated extension of the field $\mathbb{R}$ of real numbers. In particular, we recover…

Let G be a regular Lie group which is a directed union of regular Lie groups G_i (all modelled on possibly infinite-dimensional, locally convex spaces). We show that G is the direct limit of the G_i as a regular Lie group whenever G admits…

We prove that a hypergroup admitting a countable basis and an invariant Haar measure has normed convergence property if and only if it is compact.

For Classical compact Lie groups, we use Macdonald's formula \cite{Ma} and Ricci curvature for analyzing a "concentration locus", which is a tool to detect where a sequence of metric, Borel measurable spaces concentrates its measure.

We study analogues of Cartan decompositions of Lie groups for totally disconnected locally compact groups. It is shown using these decompositions that a large class of totally disconnected locally compact groups acting on trees and…