Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems

TY - JOUR

T1 - Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems

AU - Nest, Ryszard

AU - Tsygan, Boris

N1 - Keywords: math.QA

PY - 2001

Y1 - 2001

N2 - Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely the Poisson structures coming from symplectic Lie algebroids, as well as holomorphic symplectic structures. For deformations of these structures we prove the classification theorems and a general a general index theorem.

AB - Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely the Poisson structures coming from symplectic Lie algebroids, as well as holomorphic symplectic structures. For deformations of these structures we prove the classification theorems and a general a general index theorem.

M3 - Journal article

SN - 1093-6106

VL - 5

JO - Asian Journal of Mathematics

JF - Asian Journal of Mathematics

IS - 4

ER -