Related papers: Lie groupoids of mappings taking values in a Lie g…

We establish the exponential law for suitably topologies on spaces of vector-valued smooth functions on topological groups, where smoothness is defined by using differentiability along continuous one-parameter subgroups. As an application,…

We show that proper Lie groupoids are locally linearizable. As a consequence, the orbit space of a proper Lie groupoid is a smooth orbispace (a Hausdorff space which locally looks like the quotient of a vector space by a linear compact Lie…

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…

Given a locally convex space $(\mathcal{A},\tau)$ with a Hausdorff locally convex topology $\tau$ such that the following maps are continuous; $u \mapsto u^*$ for all $u \in \mathcal{A}$, $x \mapsto x\cdot y$ and $x \mapsto z\cdot x$ for…

The purpose of this paper is to propose a version of the notion of convenient Lie groupoid as a generalization of this concept in finite dimension. The authors point out which obstructions appear in the infinite dimensional context and how…

Object of investigation are almost hypercomplex manifolds with Hermitian-Norden metrics of the lowest dimension. The considered manifolds are constructed on 4-dimensional Lie groups. It is established a relation between the classes of a…

In recent years methods for the integration of Poisson manifolds and of Lie algebroids have been proposed, the latter being usually presented as a generalization of the former. In this note it is shown that the latter method is actually…

Weil prolongations of a Lie group are naturally Lie groups. It is not known in the theory of infinite-dimensional Lie groups how to construct a Lie group with a given Lie algebra as its Lie algebra or whether there exists such a Lie group…

Using the Lie derivative of the metric we define a class of Lie algebras of vector fields by generalising the concept of Killing vectors. As a Lie algebra they define locally a group action on the pseudo-Riemannian manifold through…

In this paper, we develop a new and efficient approach to the computation of envelope surfaces. We interpret one-parameter systems of surfaces as curves in the homogeneous spaces of suitable Lie groups. Using the formalism of Lie groups and…

We provide a complete solution to the problem of extending a local Lie groupoid to a global Lie groupoid. First, we show that the classical Mal'cev's theorem, which characterizes local Lie groups that can be extended to global Lie groups,…

This book explores geometries defined by left-invariant distance functions on Lie groups, with a particular focus on nilpotent groups and Carnot groups equipped with geodesic distances. Geodesic left-invariant metrics are either…

We study some basic analytic questions related to differential operators on Lie manifolds, which are manifolds whose large scale geometry can be described by a a Lie algebra of vector fields on a compactification. We extend to Lie manifolds…

Orthogonal Lie algebras in dimension 4 are identified as current Lie algebras, thus producing a natural decomposition for them over any field.

As announced in [12], we develop a calculus of Fourier integral G-operators on any Lie groupoid G. For that purpose, we study convolability and invertibility of Lagrangian conic submanifolds of the symplectic groupoid T * G. We also…

We use the general setting for contrast (potential) functions in statistical and information geometry provided by Lie groupoids and Lie algebroids. The contrast functions are defined on Lie groupoids and give rise to two-forms and…

Alain Connes introduced the use of Lie groupoids in noncommutative geometry in his pioneering work on the index theory of foliations. In the present paper, we recall the basic notion involved: groupoids, their C*-algebras, their…

We construct a new family of infinite-dimensional quasi-graded Lie algebras on hyperelliptic curves. We show that constructed algebras possess infinite number of invariant functions and admit a decomposition into the direct sum of two…

A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and…

This work is a spin-off of an on-going programme which aims at revisiting the original studies of Lie and Cartan on pseudogroups and geometric structures from a modern perspective. We encode geometric structures induced by transitive Lie…