Twist star products and Morita equivalence

Abstract

We present a simple no-go theorem for the existence of a deformation quantization of a homogeneous space M induced by a Drinfel'd twist: we argue that equivariant line bundles on M with non-trivial Chern class and symplectic twist star products cannot both exist on the same manifold M. This implies, for example, that there is no symplectic star product on the complex projective spaces induced by a twist based on U(gl(n,C))[[h]] or any sub-bialgebra, for every n greater or equal than 2.

arXiv comment10 pages, no figures

References in corpus (17)

• Deformation quantization of Poisson manifolds, I
• Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to \infty$
• Noncommutative Geometry and Gravity
• Quantum groupoids
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Matrix algebras converge to the sphere for quantum Gromov--Hausdorff distance
• The characteristic classes of Morita equivalent star products on symplectic manifolds
• Berezin-Toeplitz quantization for compact Kaehler manifolds. A Review of Results
• On second quantization on noncommutative spaces with twisted symmetries
• Deformation quantization of compact Kaehler manifolds by Berezin-Toeplitz quantization
• Semiclassical Geometry of Quantum Line Bundles and Morita Equivalence of Star Products
• Dirac operators for coadjoint orbits of compact Lie groups
• Twisting all the way: from algebras to morphisms and connections
• Deformation Quantization of Hermitian Vector Bundles
• Star Product Geometries
• Deformation Quantization of Surjective Submersions and Principal Fibre Bundles
• Topics in Noncommutative Geometry

Cited by in corpus (4)

• Braided Cartan Calculi and Submanifold Algebras
• Twisted submanifolds of R^n
• Twisted Quadrics and Algebraic Submanifolds in ${\mathbb{R}}^n$
• Characteristic (Fedosov-)class of a twist constructed by Drinfel'd