Modular vector fields and Batalin-Vilkovisky algebras

Yvette Kosmann-Schwarzbach

Banach Center Publications (2000)

  • Volume: 51, Issue: 1, page 109-129
  • ISSN: 0137-6934

Abstract

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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 d P -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.

How to cite

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Kosmann-Schwarzbach, Yvette. "Modular vector fields and Batalin-Vilkovisky algebras." Banach Center Publications 51.1 (2000): 109-129. <http://eudml.org/doc/209022>.

@article{Kosmann2000,
abstract = {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 $d_\{P\}$-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.},
author = {Kosmann-Schwarzbach, Yvette},
journal = {Banach Center Publications},
keywords = {modular vector field; Batalin-Vilkovisky algebra; triangular Lie bialgebroid; orientable Poisson manifold; generating operators; Gerstenhaber algebra; right actions; left actions; characteristic class of a Lie algebroid},
language = {eng},
number = {1},
pages = {109-129},
title = {Modular vector fields and Batalin-Vilkovisky algebras},
url = {http://eudml.org/doc/209022},
volume = {51},
year = {2000},
}

TY - JOUR
AU - Kosmann-Schwarzbach, Yvette
TI - Modular vector fields and Batalin-Vilkovisky algebras
JO - Banach Center Publications
PY - 2000
VL - 51
IS - 1
SP - 109
EP - 129
AB - 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 $d_{P}$-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.
LA - eng
KW - modular vector field; Batalin-Vilkovisky algebra; triangular Lie bialgebroid; orientable Poisson manifold; generating operators; Gerstenhaber algebra; right actions; left actions; characteristic class of a Lie algebroid
UR - http://eudml.org/doc/209022
ER -

References

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