Modular classes of Lie algebroid morphisms

Details Modular classes of Lie algebroid morphisms Modular classes of Lie algebroid morphisms

2007-12-18

arxiv.org/abs/0712.3021v2

Mathematics

Differential Geometry

33 pages. Dedicated to Bertram Kostant for his eightieth birthday. Minor changes in version 2: Proposition 3.11 added, typos c

Scientific paper

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.

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