Related papers: On stable Cartan subgroups of Lie groups

We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…

We study the automorphisms of modular curves associated to Cartan subgroups of $\mathrm{GL}_2(\mathbb Z/n\mathbb Z)$ and certain subgroups of their normalizers. We prove that if $n$ is large enough, all the automorphisms are induced by the…

If $\mathfrak{g} \subseteq \mathfrak{h}$ is an extension of Lie algebras over a field $k$ such that ${\rm dim}_k (\mathfrak{g}) = n$ and ${\rm dim}_k (\mathfrak{h}) = n + m$, then the Galois group ${\rm Gal} \, (\mathfrak{h}/\mathfrak{g})$…

The reduced $C^*$-algebra of the interior of the isotropy in any Hausdorff \'etale groupoid $G$ embeds as a $C^*$-subalgebra $M$ of the reduced $C^*$-algebra of $G$. We prove that the set of pure states of $M$ with unique extension is…

We give simple and unified proofs of the known stability and rigidity results for Lie algebras, Lie subalgebras and Lie algebra homomorphisms. Moreover, we investigate when a Lie algebra homomorphism is stable under all automorphisms of the…

Let $(Z,\omega)$ be a \Keler manifold and let $U$ be a compact connected Lie group with Lie algebra $\mathfrak{u}$ acting on $Z$ and preserving $\omega$. We assume that the $U$-action extends holomorphically to an action of the complexified…

For a locally compact metrizable group $G$, we study the action of $\rm Aut(G)$ on $\rm Sub_G$, the set of closed subgroups of $G$ endowed with the Chabauty topology. Given an automorphism $T$ of $G$, we relate the distality of the…

Let G be a Lie group, $T^*G$ its cotangent bundle with its natural Lie group structure obtained by performing a left trivialization of T^*G and endowing the resulting trivial bundle with the semi-direct product, using the coadjoint action…

In this paper we show that topological subgroupoids of Lie groupoids, under special circumstances are Lie subgroupoids. Giving an example, we indicate that having the same topological dimension is a necessary condition for topological…

Given a Lie group $G$ with finitely many components and a compact Lie group A which acts on $G$ by automorphisms, we prove that there always exists an A-invariant maximal compact subgroup K of G, and that for every such K, the natural map…

The compact simply connected Riemannian 4-symmetric spaces were classified by J.A. Jim{\'{e}}nez according to type of the Lie algebras. As homogeneous manifolds, these spaces are of the form $G/H$, where $G$ is a connected compact simple…

Let $M$ be a finite volume analytic pseudo-Riemannian manifold that admits an isometric $G$-action with a dense orbit, where $G$ is a connected non-compact simple Lie group. For low-dimensional $M$, i.e. $\dim(M) < 2\dim(G)$, when the…

A Lie algebra $\mathfrak{g}_\mathbb{Q}$ over $\mathbb{Q}$ is said to be $\mathbb{R}$-universal if every homomorphism from $\mathfrak{g}_\mathbb{Q}$ to $\mathfrak{gl}(n,\mathbb{R})$ is conjugate to a homomorphism into…

Left invariant affine structures in a Lie group $G$ are in one-to-one correspondence with left-symmetric algebras over its Lie algebra $\mathfrak g=T_eG$ (``over'' means that the commutator $[x,y]=xy-yx$ coincides with the Lie bracket;…

We consider a problem whether a given Lie group can be realized as the group of all biholomorphic automorphisms of a bounded domain in the affine complex space. In an earlier paper of 1990, we proved the result for connected linear Lie…

Let K be a number field. For any system of semisimple mod l Galois representations {\phi_l:Gal_K->GL_N(F_l)} arising from \'etale cohomology, there exists a finite normal extension L of K such that if we denote \phi_l(Gal_K) and…

The semi-classical spectrum of the Homogeneous sine-Gordon theories associated with an arbitrary compact simple Lie group G is obtained and shown to be entirely given by solitons. These theories describe quantum integrable massive…

We consider compact locally symmetric spaces $\Gamma\backslash G/H$ where $G/H$ is a non-compact semisimple symmetric space and $\Gamma$ is a discrete subgroup of $G$. We discuss some features of the joint spectrum of the (commutative)…

Let G be a Lie group with Lie algebra $\mathfrak{g}$, $h \in \frak{g}$ an element for which the derivation ad(h) defines a 3-grading of $\mathfrak{g}$ and $\tau_G$ an involutive automorphism of G inducing on $\mathfrak{g}$ the involution…

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…