# Modular vector fields and Batalin-Vilkovisky algebras

Banach Center Publications (2000)

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

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topKosmann-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 -

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