Twist star products and Morita equivalence

TL;DR

The paper proves a no-go theorem showing that certain geometric structures and twist-induced deformation quantizations cannot coexist on the same homogeneous space, impacting the existence of symplectic star products on complex projective spaces.

Contribution

It establishes a fundamental obstruction to combining equivariant line bundles with non-trivial Chern class and twist star products on homogeneous spaces.

Findings

No symplectic twist star product on complex projective spaces from U(gl(n,C))[[h]]

Obstruction applies to all n ≥ 2

Impacts deformation quantization approaches for homogeneous spaces

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.