Related papers: Virtual Lie subgroups of locally compact groups

We define a local Sylow subgroup of a totally disconnected, locally compact group G to be a maximal pro-p subgroup of an open compact subgroup of G. We use these subgroups to define the p-localisation of G, a locally virtually pro-p group…

We conjecture that the automorphism group of a topological parallelism on real projective 3-space is compact. We prove that at least the identity component of this group is, indeed, compact.

If an open subgroup of the group of the invertible measures on a LCA group is isometric to another, then the correspoinding underlying LCA groups are topologically isomorphic to each other.

We study expressive power of continuous logic in classes of (locally compact) groups. We also describe locally compact groups which are separably categorical structures.

We study homogeneous metric spaces, by which we mean connected, locally compact metric spaces whose isometry group acts transitively. After a review of some classical results, we use the Gleason-Iwasawa-Montgomery-Yamabe-Zippin structure…

We describe the global structure of totally disconnected locally compact groups having a linear open compact subgroup. Among the applications, we show that if a non-discrete, compactly generated, topologically simple, totally disconnected…

In this article we provide evidence for a well-known conjecture which states that quasi-isometric simply-connected nilpotent Lie groups are isomorphic. We do so by constructing new examples which are rigid in the sense that whenever they…

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…

Here, we classify Lie groups acting isometrically on compact Lorentz manifolds, and in particular we describe the geometric structure of compact homogeneous Lorentz manifolds.

We study properties and the structure of Cartan subgroups in a connected Lie group. We obtain a characterisation of Cartan subgroups which generalises W\"ustner's structure theorem for the same. We show that Cartan subgroups are same as…

We study the real spectrum compactification of character varieties of finitely generated groups in semisimple Lie groups. This provides a compactification with good topological properties, and we interpret the boundary points in terms of…

We study topological groups having all closed subgroups (totally) minimal and we call such groups c-(totally) minimal. We show that a locally compact c-minimal connected group is compact. Using a well-known theorem of Hall and Kulatilaka…

We continue the analysis of definably compact groups definable in a real closed field $\mathcal{R}$. In [3], we proved that for every definably compact definably connected semialgebraic group $G$ over $\mathcal{R}$ there are a connected…

We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…

We fill in the details in a procedure outlined by Serre for drawing pictures of compact real Lie groups. In the case of Sp($2n$), the picture generated by the method is connected with abelian varieties over a number field or a finite field.…

The notion of an open quantum subgroup of a locally compact quantum group is introduced and given several equivalent characterizations in terms of group-like projections, inclusions of quantum group C*-algebras and properties of respective…

A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…

Let $G_1$ and $G_2$ be Lie groups furnished with bi-invariant metrics and $f:G_1\rightarrow G_2$ be a Lie group homomorphism which is also a minimal isometric immersion. If $G_1$ is compact and connected, we prove that either $G_1$ is…

To each totally disconnected, locally compact topological group G and each group A of automorphisms of G, a pseudo-metric space of ``directions'' has been associated by U. Baumgartner and the second author. Given a Lie group G over a local…

We show that, in compact semisimple Lie groups and Lie algebras, any neighbourhood of the identity gets mapped, under the commutator map, to a neighbourhood of the identity.