Star products with separation of variables admitting a smooth extension

Abstract

Given a complex manifold $M$ with an open dense subset $\Omega$ endowed with a pseudo-Kaehler form $\omega$ which cannot be smoothly extended to a larger open subset, we consider various examples where the corresponding Kaehler-Poisson structure and a star product with separation of variables on $(\Omega ,\omega )$ admit smooth extensions to $M$. We suggest a simple criterion of the existence of a smooth extension of a star product and apply it to these examples.

17 pages, some additions and corrections made

References in corpus (1)

• Deformation quantization of a Kaehler-Poisson structure vanishing on a Levi nondegenerate hypersurface