9 citations · 13 across the 4 of their papers we have counts for
4 papers
The Local Structure of Lie Bialgebroids
Zhang-Ju Liu, Ping Xu
We study the local structure of Lie bialgebroids at regular points. In particular, we classify all transitive Lie bialgebroids. In special cases, they are connected to classical dy…
Dirac structures and dynamical r-matrices
Zhang-Ju Liu, Ping Xu
The purpose of this paper is to establish a connection between various subjects such as dynamical r-matrices, Lie bialgebroids, and Lagrangian subalgebras. Our method relies on the…
Dirac structures and Poisson homogeneous spaces
Z. J. Liu, A. Weinstein, P. Xu
Poisson homogeneous spaces for Poisson groupoids are classfied in terms of Dirac structures for the corresponding Lie bialgebroids. Applications include Drinfel'd's classification…
Manin Triples for Lie Bialgebroids
Zhang-Ju Liu, Alan Weinstein, Ping Xu
In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms…