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… (More)

– In this paper, we develop twisted K-theory for stacks, where the twisted class is given by an S-gerbe over the stack. General properties, including the Mayer–Vietoris property, Bott periodicity,… (More)

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 algebras… (More)

The purpose of the paper is to study various aspects of star products on a symplectic manifold related to the Fedosov method. By introducing the notion of “quantum exponential maps”, we give a… (More)

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 include also the… (More)

Poisson homogeneous spaces for Poisson groupoids are classfied in terms of Dirac structures for the corresponding Lie bialgebroids. Applications include Drinfel’d’s classification in the case of… (More)

Poisson manifolds may be regarded as the infinitesimal form of symplectic groupoids. Twisted Poisson manifolds considered by Image Severa and Weinstein [Prog. Theor. Phys. Suppl. 144 (2001) 145] are… (More)

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 bialgebroid as a… (More)

By using twist construction, we obtain a quantum groupoid D⊗qUqg for any simple Lie algebra g. The underlying Hopf algebroid structure encodes all the information of the corresponding elliptic… (More)

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 the de Rham… (More)