The Van den Bergh duality and the modular symmetry of a Poisson variety |
| |
Authors: | Vasiliy Dolgushev |
| |
Affiliation: | (1) Department of Mathematics, Northwestern University Evanston, Evanston, IL 60208, USA |
| |
Abstract: | We consider a smooth Poisson affine variety with the trivial canon-ical bundle over . For such a variety the deformation quantization algebra obeys the conditions of the Van den Bergh duality theorem and the corresponding dualizing module is determined by an outer automorphism of intrinsic to . We show how this automorphism can be expressed in terms of the modular class of the corresponding Poisson variety. We also prove that the Van den Bergh dualizing module of the deformation quantization algebra is free if and only if the corresponding Poisson structure is unimodular. |
| |
Keywords: | KeywordHeading" >Mathematics Subject Classification (2000). 55U30 53D55 18G15 |
本文献已被 SpringerLink 等数据库收录! |