相关论文: Prequantization and Lie brackets

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 generalize the prequantization central extension of a group of diffeomorphisms preserving a closed 2-form \omega (\omega-invariant diffeomorphisms) to an abelian extension of a group of diffeomorphisms preserving a closed vector valued…

We begin with a short presentation of the basic concepts related to Lie groupoids and Lie algebroids, but the main part of this paper deals with Lie algebroids. A Lie algebroid over a manifold is a vector bundle over that manifold whose…

We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…

If {\omega} is a closed G-invariant 2-form and {\mu} a moment map, then we obtain necessary and sufficient conditions for equivariant pre-quantizability that can be computed in terms of the moment map {\mu}. We also compute the obstructions…

For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation…

In this survey, we discuss a series of linearization problems--for Poisson structures, Lie algebroids, and Lie groupoids. The last problem involves a conjecture on the structure of proper groupoids. Attempting to prove this by the method of…

A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of…

We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid. We also have a closer look at various special cases…

We consider the pair of degenerate compatible antibrackets satisfying a generalization of the axioms imposed in the triplectic quantization of gauge theories. We show that this actually encodes a Lie group structure, with the antibrackets…

Given a Poisson (or more generally Dirac) manifold $P$, there are two approaches to its geometric quantization: one involves a circle bundle $Q$ over $P$ endowed with a Jacobi (or Jacobi-Dirac) structure; the other one involves a circle…

We survey recent results on the local and global integrability of a Lie algebroid, as well as the integrability of infinitesimal multiplicative geometric structures on it.

In this paper we study quotients of Lie algebroids and groupoids endowed with compatible differential forms. We identify Lie theoretic conditions under which such forms become basic and characterize the induced forms on the quotients. We…

We construct Hermitian representations of Lie algebroids and associated unitary representations of Lie groupoids by a geometric quantization procedure. For this purpose we introduce a new notion of Hamiltonian Lie algebroid actions. The…

Contents * Introduction -- Why $S^1$-extended phase space? -- Why central extensions of classical symmetries? * Central extension \Gt of a group $G$ -- Group cohomology -- Cohomology and contractions: Pseudo-cohomology -- Principal bundle…

We define a general notion of abstract double Lie algebroid. We show (1) that the double Lie algebroid of a double Lie groupoid is a double Lie algebroid in this sense; (2) that the double cotangent constructed from Lie algebroid structures…

We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucidate the Lie theory relating these objects, i.e., their…

Natural analogs of Lie brackets on affine bundles are studied, based on natural examples from differential geometry and analytical mechanics. In particular, a close relation to Lie algebroids and, by a sort of duality, to affine analogs of…

Given a Lie algebroid we discuss the existence of a smooth abelian integration of its abelianization. We show that the obstructions are related to the extended monodromy groups introduced recently in \cite{CFMb}. We also show that this…

Let G be a Lie groupoid with Lie algebroid g. It is known that, unlike in the case of Lie groups, not every subalgebroid of g can be integrated by a subgroupoid of G. In this paper we study conditions on the invariant foliation defined by a…