165 citations · 1.1k across the 63 of their papers we have counts for
6 papers · 1 filter
Integration of Lie bialgebroids
Kirill C. H. Mackenzie, Ping Xu
We prove that under certain mild assumptions a Lie bialgebroid integrates to a Poisson groupoid. This includes, in particular, a new proof of the existence of local symplectic grou…
Classical lifting processes and multiplicative vector fields
Kirill Mackenzie, Ping Xu
We extend the calculus of multiplicative vector fields and differential forms and their intrinsic derivatives from Lie groups to Lie groupoids; this generalization turns out to inc…
Hochschild cohomology and characteristic classes for star-products
Alan Weinstein, Ping Xu
We show that the Hochschild cohomology of the algebra obtained by formal deformation quantization on a symplectic manifold is isomorphic to the formal series with coefficients in t…
Quantum groupoids and deformation quantization
Ping Xu
The purpose of this Note is to unify quantum groups and star-products under a general umbrella: quantum groupoids. It is shown that a quantum groupoid naturally gives rise to a Lie…
Gerstenhaber algebras and BV-algebras in Poisson geometry
Ping Xu
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 Gerst…
Pseudodifferential operators on differential groupoids
Victor Nistor, Alan Weinstein, Ping Xu
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 con…