We show that a modular class arises from the existence of two generating operators for a Batalin-Vilkovisky algebra. In particular, for every triangular Lie bialgebroid (A,P) such that its top exterior power is a trivial line bundle, there is a section of the vector bundle A whose -cohomology class is well-defined. We give simple proofs of its properties. The modular class of an orientable Poisson manifold is an example. We analyse the relationships between generating operators of the Gerstenhaber algebra of a Lie algebroid, right actions on the elements of degree 0, and left actions on the elements of top degree. We show that the modular class of a triangular Lie bialgebroid coincides with the characteristic class of a Lie algebroid with representation on a line bundle.
@article{bwmeta1.element.bwnjournal-article-bcpv51z1p109bwm,
author = {Kosmann-Schwarzbach, Yvette},
title = {Modular vector fields and Batalin-Vilkovisky algebras},
journal = {Banach Center Publications},
volume = {51},
year = {2000},
pages = {109-129},
zbl = {1018.17020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p109bwm}
}
Kosmann-Schwarzbach, Yvette. Modular vector fields and Batalin-Vilkovisky algebras. Banach Center Publications, Tome 51 (2000) pp. 109-129. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p109bwm/
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