Jacobi-Dirac结构及其特征对、对偶特征对

Jacobi-Dirac structure and its characteristic pairs and dual characteristic pairs

将李双代数胚的Dirac结构推广到Jacobi双代数胚的Jacobi-Dirac结构;同时,将Dirac结构的特征对推广到Jacobi-Dirac结构的特征对,并给出其对偶特征对。有了这些工具,利用Dirac结构进行Poisson流形的约化即可对应地推广到利用Jacobi-Dirac结构进行Jacobi流形的约化。

The Dirac structure of Lie bialgebroid is generalized to Jacobi-Dirac structure of Jacobi bialgebroid. Meanwhile, the characteristic pair and dual characteristic pair are also generalized to those of Jacobi-Dirac structure, with which the reduction of Jacobi manifolds can be processed as those of Poisson manifolds.