Generalized Lie bialgebroids and Jacobi structures

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 h as associated a canonical generalized Lie bialgebroid. As a kind of convers e, we prove that a Jacobi structure can be defined on the base space of a g eneralized 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 L ie bialgebroids are considered: triangular generalized Lie bialgebroids and generalized Lie bialgebras. (C) 2001 Elsevier Science BN. All rights reser ved.