منابع مشابه
Groupoids and the Integration of Lie Algebroids
We show that a Lie algebroid on a stratified manifold is integrable if, and only if, its restriction to each strata is integrable. These results allow us to construct a large class of algebras of pseudodifferential operators. They are also relevant for the definition of the graph of certain singular foliations of manifolds with corners and the construction of natural algebras of pseudodifferent...
متن کاملThe integration problem for complex Lie algebroids
A complex Lie algebroid is a complex vector bundle over a smooth (real) manifold M with a bracket on sections and an anchor to the complexified tangent bundle of M which satisfy the usual Lie algebroid axioms. A proposal is made here to integrate analytic complex Lie algebroids by using analytic continuation to a complexification of M and integration to a holomorphic groupoid. A collection of d...
متن کاملInvariants of Lie algebroids
Several new invariants of Lie algebroids have been discovered recently. We give an overview of these invariants and establish several relationships between them.
متن کاملLie Algebroids and Lie Pseudoalgebras
Lie algebroids and Lie pseudoalgebras arise from a wide variety of constructions in differential geometry; they have been introduced repeatedly into the geometry, physics and algebra literatures since the 1950s, under some 14 different terminologies. The first main part (Sections 2-5) of this survey describes the four principal classes of examples, emphazising that each arises by means of a gen...
متن کاملHorizontal Subbundle on Lie Algebroids
Providing an appropriate definition of a horizontal subbundle of a Lie algebroid will lead to construction of a better framework on Lie algebriods. In this paper, we give a new and natural definition of a horizontal subbundle using the prolongation of a Lie algebroid and then we show that any linear connection on a Lie algebroid generates a horizontal subbundle and vice versa. The same correspo...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2009
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-009-0388-7