, Volume 13, Issue 3-4, pp 727-755
Date: 20 Sep 2008

Modular Classes of Lie Algebroid Morphisms

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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.

Dedicated to Bertram Kostant on the occasion of his eightieth birthday