Related papers: Pro-Lie groups which are infinite-dimensional Lie …

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…

The paper presents the complete classification of Automorphic Lie Algebras based on $\mathfrak{sl}_n (\mathbb{C})$, where the symmetry group $G$ is finite and the orbit is any of the exceptional $G$-orbits in $\overline{\mathbb{C}}$. A key…

Let $G$ be a connected semisimple noncompact real Lie group and let $\rho: G \longrightarrow \mathrm{SL}(V)$ be a representation on a finite dimensional vector space $V$ over $\mathbb R$, with $\rho(G)$ closed in $\mathrm{SL}(V)$.…

We study algebraic properties of groups of PL or smooth homeomorphisms of unit cubes in any dimension, fixed pointwise on the boundary, and more generally PL or smooth groups acting on manifolds and fixing pointwise a submanifold of…

Presentations of smooth symmetry groups of differentiable stacks are studied within the framework of the weak 2-category of Lie groupoids, smooth principal bibundles, and smooth biequivariant maps. It is shown that principality of bibundles…

Every finite dimensional real representation of a compact real semisimple Lie algebra determines a metric 2-step nilpotent Lie algebra and a corresponding simply connected metric 2-step nilpotent Lie group N. We study the differential…

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…

Necessary or sufficient conditions are presented for the existence of various types of actions of Lie groups and Lie algebras on manifolds.

The object of investigation are Lie groups considered as almost contact B-metric manifolds of the lowest dimension three. It is established a correspondence of all basic-class-manifolds of the Ganchev-Mihova-Gribachev classification of the…

A finitely generated subgroup {\Gamma} of a real Lie group G is said to be Diophantine if there is \beta > 0 such that non-trivial elements in the word ball B_\Gamma(n) centered at the identity never approach the identity of G closer than…

A Lie algebra L is known to be nilpotent if it admits a grading by (Zp, +) with support X not containing 0. It is also known that the class of L can be bounded by some explicit function of |X|. We generalise this and other classical results…

We study the link between stably finiteness and stably projectionless-ness for $C^*$-algebras of solvable Lie groups. We show that these two properties are equivalent if the dimension of the group is not divisible by $4$; otherwise, they…

For a prime $p$, a $p$-subgroup of a finite group $G$ is said to be large if and only if $Q= F^*(N_G(Q))$ and, for all $1 \neq U \le Z(Q)$, $N_G(U) \le N_G(Q)$. In this article we determine those groups $G$ which have a large subgroup and…

For a stratified group $G$, we construct a class of polarised Lie groups, which we call modifications of $G$, that are locally contactomorphic to it. Vice versa, we show that if a polarised group is locally contactomorphic to a stratified…

Half Lie groups exist only in infinite dimensions: They are smooth manifolds and topological groups such that right translations are smooth, but left translations are merely required to be continuous. The main examples are groups of $H^s$…

A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called locally precompact. Within the class of locally…

An almost Abelian Lie group is a non-Abelian Lie group with a codimension 1 Abelian subgroup. We show that all discrete subgroups of complex simply connected almost Abelian groups are finitely generated. The topology of connected almost…

Given a compact Lie group $G$ with Lie algebra $\mathfrak{g}$, we consider its tangent Lie group $TG\cong G\ltimes_{\mathrm{Ad}} \mathfrak{g}$. In this short note, we prove that $TG$ admits a left-invariant naturally reductive Riemannian…

In this paper, we introduce the notion of compatible anti-pre-Lie algebras and study relationship between them and the related structures such as anti-$\mathcal{O}$-operators, commutative $2$-cocycles on compatible Lie algebras. Moreover,…

Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold…