Related papers: A unified proof of the Howe-Moore property

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…

We define a Howe-Moore property relative to a set of subgroups. Namely, a group $G$ has the Howe-Moore property relative to a set $\mathcal{F}$ of subgroups if for every unitary representation $\pi$ of $G$, whenever the restriction of $\pi$…

We formulate and study Howe-Moore type properties in the setting of quantum groups and in the setting of rigid $C^{\ast}$-tensor categories. We say that a rigid $C^{\ast}$-tensor category $\mathcal{C}$ has the Howe-Moore property if every…

Firstly, we prove that every closed subgroup $H$ of type-preserving automorphisms of a locally finite thick affine building $\Delta$ of dimension $\geq 2$ that acts strongly transitively on $\Delta$ is Moufang. If moreover $\Delta$ is…

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…

We prove that if a unitary representation of a connected Lie group has the property that no nonozero vector is fixed by any nontrival normal connected subgroup, then the matrix coefficients decay to zero at Adjoint-infinity.

We establish a fixed point property for a certain class of locally compact groups, including almost connected Lie groups and compact groups of finite abelian width, which act by simplicial isometries on finite rank buildings with measurable…

Let $T$ be a locally finite tree all of whose vertices have valency at least $6$. We classify, up to isomorphism, the closed subgroups of $\mathrm{Aut}(T)$ acting $2$-transitively on the set of ends of $T$ and whose local action at each…

In \cite{Kramer11} Kramer proves for a large class of semisimple Lie groups that they admit just one locally compact $\sigma$-compact Hausdorff topology compatible with the group operations. We present two different methods of generalising…

This thesis is devoted to the study of the interactions existing between the algebraic structure of locally compact groups and the properties of their continuous unitary representations, with a special emphasis on the Type I groups. On the…

We establish two structural results for Moore homology of ample groupoids. First, for every ample groupoid $\mathcal{G}$ and every discrete abelian coefficient group $A$, we prove a universal coefficient theorem relating the homology groups…

The unitary representation theory of locally compact contraction groups and their semi-direct products with $\mathbb{Z}$ is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this…

We study generic properties of topological groups in the sense of Baire category. First we investigate countably infinite (discrete) groups. We extend a classical result of B. H. Neumann, H. Simmons and A. Macintyre on algebraically closed…

We study algebraic properties on a group G such that if the discrete group G has these properties then every locally compact shift continuous topology on G with adjoined zero is either compact, or discrete. We introduce electorally flexible…

We study homology of ample groupoids via the compactly supported Moore complex of the nerve. Let $A$ be a topological abelian group. For $n\ge 0$ set $C_n(\mathcal G;A) := C_c(\mathcal G_n,A)$ and define…

We show that the convolution algebra of smooth, compactly-supported functions on a Lie groupoid is H-unital in the sense of Wodzicki. We also prove H-unitality of infinite order vanishing ideals associated to invariant, closed subsets of…

Considering modules of finite complete intersection dimension over commutative Noetherian local rings, we prove (co)homology vanishing results in which we assume the vanishing of nonconsecutive (co)homology groups. In fact, the (co)homology…

We establish three independent results on groups acting on trees. The first implies that a compactly generated locally compact group which acts continuously on a locally finite tree with nilpotent local action and no global fixed point is…

We characterize group compactifications of discrete groups for which there exists an equivariant retraction onto the boundary. In particular, we prove an equivariant analogue of Brouwer's No-Retraction theorem for large classes of group…

We provide characterizations of Lie groups as compact-like groups in which all closed zero-dimensional metric (compact) subgroups are discrete. The "compact-like" properties we consider include (local) compactness, (local)…