منابع مشابه
Lie algebroid structures on a class of affine bundles
We introduce the notion of a Lie algebroid structure on an affine bundle whose base manifold is fibred over IR. It is argued that this is the framework which one needs for coming to a time-dependent generalization of the theory of Lagrangian systems on Lie algebroids. An extensive discussion is given of a way one can think of forms acting on sections of the affine bundle. It is further shown th...
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We present results describing Lie ideals and maximal finite-codimensional Lie subalgebras of the Lie algebras associated with Lie algebroids with non-singular anchor maps. We also prove that every isomorphism of such Lie algebras induces diffeomorphism of base manifolds respecting the generalized foliations defined by the anchor maps.
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We prove some general results about the relation between the 1-cocycles of an arbitrary Lie algebroid A over M and the leaves of the Lie algebroid foliation on M associated with A. Using these results, we show that a E1(M)-Dirac structure L induces on every leaf F of its characteristic foliation a E1(F )-Dirac structure LF , which comes from a precontact structure or from a locally conformal pr...
متن کاملLie algebroid structures and Lagrangian systems on affine bundles
As a continuation of previous papers, we study the concept of a Lie algebroid structure on an affine bundle by means of the canonical immersion of the affine bundle into its bidual. We pay particular attention to the prolongation and various lifting procedures, and to the geometrical construction of Lagrangian-type dynamics on an affine Lie algebroid.
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We show that the path construction integration of Lie algebroids by Lie groupoids is an actual equivalence from the of integrable Lie algebroids and complete Lie algebroid comorphisms to the of source 1-connected Lie groupoids and Lie groupoid comorphisms. This allows us to construct an actual symplectization functor in Poisson geometry. We include examples to show that the integrability of com...
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ژورنال
عنوان ژورنال: International Journal of Geometric Methods in Modern Physics
سال: 2005
ISSN: 0219-8878,1793-6977
DOI: 10.1142/s0219887805000909