标题： 广义李双代数和雅可比结构 显示英文标题

标题： Generalized Lie bialgebroids and Jacobi structures

摘要： 广义李双代数（李双代数概念的推广）的概念被以这样的方式引入，使得雅可比流形关联有一个典型的广义李双代数。 作为某种逆命题，我们证明可以在广义李双代数的基空间上定义一个雅可比结构。 我们还表明，可以从一个广义李双代数构造出一个李双代数，并由此推导出一个对偶定理。 最后，考虑了一些特殊的广义李双代数类别：三角形广义李双代数和广义李双代数。 显示英文摘要

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.