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Manin Triples for Lie Bialgebroids

- Zhang-Ju Liu, A. Weinstein, P. Xu
- Mathematics
- 28 August 1995

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. This bracket does… Expand

Lie bialgebroids and Poisson groupoids

- K. Mackenzie, P. Xu
- Mathematics
- 1 February 1994

Lie bialgebras arise as infinitesimal invariants of Poisson Lie groups. A Lie bialgebra is a Lie algebra g with a Lie algebra structure on the dual g∗ which is compatible with the Lie algebra g in a… Expand

Gerstenhaber Algebras and BV-Algebras in Poisson Geometry

- P. Xu
- Mathematics
- 1 March 1997

Abstract:The purpose of this paper is to establish an explicit correspondence between various geometric structures on a vector bundle with some well-known algebraic structures such as Gerstenhaber… Expand

Pseudodifferential operators on differential groupoids

- V. Nistor, A. Weinstein, P. Xu
- Mathematics
- 11 February 1997

We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction… Expand

Universal lifting theorem and quasi-Poisson groupoids

- D. I. Ponte, C. Laurent-Gengoux, P. Xu
- Mathematics
- 19 July 2005

We prove the universal lifting theorem: for an α-simply connected and α-connected Lie groupoid with Lie algebroid A, the graded Lie algebra of multi-differentials on A is isomorphic to that of… Expand

Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids

- C. Laurent-Gengoux, M. Stiénon, P. Xu
- Mathematics
- 28 July 2007

We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson… Expand

Morita equivalence of Poisson manifolds

- P. Xu
- Mathematics
- 1 December 1991

Poisson manifolds are the classical analogue of associative algebras. For Poisson manifolds, symplectic realizations play a similar role as representations do for associative algebras. In this paper,… Expand

On Regular Courant Algebroids

- Zhuo Chen, M. Stiénon, P. Xu
- Mathematics
- 2 September 2009

For any regular Courant algebroid, we construct a characteristic class a la Chern-Weil. This intrinsic invariant of the Courant algebroid is a degree-3 class in its naive cohomology. When the Courant… Expand

Poisson Quasi-Nijenhuis Manifolds

- M. Stiénon, P. Xu
- Mathematics
- 14 February 2006

We introduce the notion of Poisson quasi-Nijenhuis manifolds generalizing Poisson-Nijenhuis manifolds of Magri-Morosi. We also investigate the integration problem of Poisson quasi-Nijenhuis… Expand

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