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.
Twist star products and Morita equivalence / D'Andrea, Francesco; Weber, Thomas. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 355:11(2017), pp. 1178-1184. [10.1016/j.crma.2017.10.012]
Twist star products and Morita equivalence
D'Andrea, Francesco
;Weber, Thomas
2017
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.