Generalized Lie bialgebroids and Jacobi structures

JOURNAL OF GEOMETRY AND PHYSICS

卷:40

Article

Iglesias, D ; Marrero, JC

关键词: Jacobi manifolds;    Poisson manifolds;    Lie algebroids;    Lie bialgebroids;    triangular Lie bialgebroids;    Lie bialgebras;   

DOI  :  10.1016/S0393-0440(01)00032-8

来源: Elsevier

【 摘 要 】

The notion of a generalized Lie bialgebroid (a generalization of the notion of a Lie bialgebroid) is introduced in such a way that a Jacobi manifold has associated a canonical generalized Lie bialgebroid. As a kind of converse, we prove that a Jacobi structure can be defined on the base space of a generalized Lie bialgebroid. We also show that it is possible to construct a Lie bialgebroid from a generalized Lie bialgebroid and, as a consequence, we deduce a duality theorem. Finally, some special classes of generalized Lie bialgebroids are considered: triangular generalized Lie bialgebroids and generalized Lie bialgebras. (C) 2001 Elsevier Science BN. All rights reserved.

【 授权许可】

Free