On the geometric quantization of twisted Poisson manifolds

Abstract

We study the geometric quantization process for twisted Poisson manifolds. First, we introduce the notion of Lichnerowicz-twisted Poisson cohomology for twisted Poisson manifolds and we use it in order to characterize their prequantization bundles and to establish their prequantization condition. Next, we introduce a polarization and we discuss the quantization problem. In each step, several examples are presented.

References in corpus (4)

• The modular class of a twisted Poisson structure
• Twisted Jacobi manifolds, twisted Dirac-Jacobi structures and quasi-Jacobi bialgebroids
• Poisson cohomology and quantization
• Modular classes of regular twisted Poisson structures on Lie algebroids

Cited by in corpus (4)

• Leibniz 2-algebras and twisted Courant algebroids
• Symplectic realisation of electric charge in fields of monopole distributions
• Nonassociative Weyl star products
• Lie 2-algebra models