Modular classes of Lie algebroid morphisms
Differential Geometry
2008-04-18 v2 Symplectic Geometry
Abstract
We study the behavior of the modular class of a Lie algebroid under general Lie algebroid morphisms by introducing the relative modular class. We investigate the modular classes of pull-back morphisms and of base-preserving morphisms associated to Lie algebroid extensions. We also define generalized morphisms, including Morita equivalences, that act on the 1-cohomology, and observe that the relative modular class is a coboundary on the category of Lie algebroids and generalized morphisms with values in the 1-cohomology.
Cite
@article{arxiv.0712.3021,
title = {Modular classes of Lie algebroid morphisms},
author = {Yvette Kosmann-Schwarzbach and Camille Laurent-Gengoux and Alan Weinstein},
journal= {arXiv preprint arXiv:0712.3021},
year = {2008}
}
Comments
33 pages. Dedicated to Bertram Kostant for his eightieth birthday. Minor changes in version 2: Proposition 3.11 added, typos corected