منابع مشابه
Lie 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...
متن کاملOmni-lie Algebroids *
A generalized Courant algebroid structure is defined on the direct sum bundle DE ⊕ JE, where DE and JE are the gauge Lie algebroid and the jet bundle of a vector bundle E respectively. Such a structure is called an omni-Lie algebroid since it is reduced to the omni-Lie algebra introduced by A.Weinstein if the base manifold is a point. We prove that any Lie algebroid structure on E is characteri...
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 Mechanics
We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the connguration manifold M; the set of units is the zero section identiied with the manifold M. We study the Legendre transformation on Lie algebroids. The purpose of this paper is not to prove new results but to investigate certain elementary tools utilized in A...
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 2001
ISSN: 0137-6934,1730-6299
DOI: 10.4064/bc54-0-3