Related papers: Flat Generalized Connections on Courant Algebroids
We investigate contact Lie groups having a left invariant Riemannian or pseudo-Riemannian metric with specific properties such as being bi-invariant, flat, negatively curved, Einstein, etc. We classify some of such contact Lie groups and…
The maximal complexifications adapted to the Levi Civita connection for a distinguished one-parameter family of left-invariant metrics on a real semisimple Lie group G are determined. For G = SL(2,R) their realizations as invariant Riemann…
In this article we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra of sections of the associated Lie…
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system on Lie algebroids are given. Here we use the general properties of Lie algebroids to express and prove two geometric version of the Hamilton-Jacobi…
We extend the notion of connection in order to be able to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual concept of connection. Using connections,…
The algebra and calculus of generalized differential forms are reviewed and employed to construct a class of generalized connections and to investigate their properties. The class includes generalized connections which are flat when…
Given a G-structure with connection satisfying a regularity assumption we associate to it a classifying Lie algebroid. This algebroid contains all the information about the equivalence problem and is an example of a G-structure Lie…
We give a new definition of Levi-Civita connection for a noncommutative pseudo-Riemannian metric on a noncommutative manifold given by a spectral triple. We prove the existence-uniqueness result for a class of modules of one forms over a…
Almost Lie algebroids are generalizations of Lie algebroids, when the Jacobiator is not necessary null. A simple example is given, for which a Lie algebroid bracket or a Courant bundle is not possible for the given anchor, but a natural…
We develop a new approach to T-duality based on Courant algebroid relations which subsumes the usual T-duality as well as its various generalisations. Starting from a relational description for the reduction of exact Courant algebroids over…
In this paper we generalize classical results on Lie algebras and universal enveloping algebras of Lie algebras to Lie-Rinehart algebras. We define for any Lie-Rinehart algebra $L$ and any cocycle $f$ in $Z^2(L,B)$, a universal enveloping…
In this paper, we establish a complete structural description of flat Lorentzian Lie groups, i.e., Lie groups endowed with a flat left invariant Lorentzian metric, thereby resolving a long-standing open problem in the theory of…
This paper investigates the geometry of compact contact manifolds that are uniformized by contact Lie groups, i.e., compact manifolds that are the quotient of some Lie group G with a left invariant contact structure and a uniform lattice…
We give a new characterization of flat affine manifolds in terms of an action of the Lie algebra of classical infinitesimal affine transformations on the bundle of linear frames. We characterize flat affine symplectic Lie groups using…
We look at generalized complex structures from the point of view of Poisson and Dirac geometry and we remark that the puzzling equations underlying the notion of generalized complex structure have miraculously simple meaning when passing to…
The notion of Lie algebroids over a topological ringed space provides a unified framework to study various geometric structures. This geometric concept is intimately connected with well-known algebraic structures, including Gerstenhaber…
We study simplicity of Lie skew braces from both global and infinitesimal perspectives. After reviewing the correspondence between connected Lie skew braces, simply transitive affine actions, and post-Lie algebras, we investigate ideals and…
Let \(X\) be an irreducible smooth complex projective variety, and let \(G\) be a connected reductive linear algebraic group over \(\mathbb{C}\). In this paper, we first classify integrable transitive algebraic Lie algebroids on $X$. We…
Let G be a connected complex Lie group. We show that any flat principal G-bundle over any finite CW-complex pulls back to a trivial bundle over some finite covering space of the base space if and only if each real characteristic class of…
A VB-algebroid is essentially defined as a Lie algebroid object in the category of vector bundles. There is a one-to-one correspondence between VB-algebroids and certain flat Lie algebroid superconnections, up to a natural notion of…