Related papers: Local and global integrability of Lie brackets
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…
This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…
We consider Lie algebroids over algebraic spaces (in short we call it as $a$-spaces) by considering the sheaf of Lie-Rinehart algebras. We discuss about properties of universal enveloping algebroid $\mathscr{U}(\mathcal{O}_X,\mathcal{L})$…
Locally conformal symplectic (l.c.s.) groupoids are introduced as a generalization of symplectic groupoids. We obtain some examples and we prove that l.c.s. groupoids are examples of Jacobi groupoids in the sense of \cite{IM}. Finally, we…
The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.
We study a few basic properties of Banach-Lie groupoids and algebroids, adapting some classical results on finite dimensional Lie groupoids. As an illustration of the general theory, we show that the notion of locally transitive Banach-Lie…
Several instances of integrable Riccati equations are analyzed from the geometric perspective of the theory of Lie systems. This provides us a unifying viewpoint for previous approaches.
We study the integrability of Poisson and Dirac structures that arise from quotient constructions. From our results we deduce several classical results as well as new applications. We also give explicit constructions of Lie groupoids…
In this paper we investigate the structure of intermediate vertex algebras associated with a maximal conformal embedding of a reductive Lie algebra in a semisimple Lie algebra of classical type.
In this article, we prove that for a definable set in an o-minimal structure with connected link (at 0 or infinity), the inner distance of the link is equivalent to the inner distance of the set restricted to the link. With this result, we…
We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…
Emerton's theory of Jacquet modules for locally analytic representations provides necessary conditions for the existence of integral structures in locally analytic representations. These conditions are also expected to be sufficient for the…
The Lie algebra specified by space of local functionals with commutator determined by the Gardner bracket was under survey. Problem of classification of deformations of this bracket over local infinitesimal transformations of functionals…
The present paper is devoted to study 2-local derivations on infinite-dimensional Lie algebras over a field of characteristic zero. We prove that all 2-local derivations on the Witt algebra as well as on the positive Witt algebra are…
Using Lie groupoids, we prove that the injectivity radius of a manifold with a Lie structure at infinity is positive.
We present a substantial generalisation of a classical result by Lie on integrability by quadratures. Namely, we prove that all vector fields in a finite-dimensional transitive and solvable Lie algebra of vector fields on a manifold can be…
In this paper I consider locally finite Lie algebras of characteristic zero satisfying the condition that for every finite number of elements $x_{1}, x_{2},..., x_{k}$ of such an algebra $L$ there is finite-dimensional subalgebra $A$ which…
We discuss natural transformations in the context of Lie groupoids, and their infinitesimal counterpart. Our main result is an integration procedure that provides smooth natural transformations between Lie groupoid morphisms.
We study the algebraic constraints on the structure of nilpotent Lie algebra $\mathbb{g}$, which arise because of the presence of an integrable complex structure $J$. Particular attention is paid to non-abelian complex structures.…
Several new invariants for Lie algebroids have been discovered recently. We give an overview of these invariants and establish several relationships between them.