Acta Applicandae Mathematica

, Volume 41, Issue 1, pp 153–165

Exact Gerstenhaber algebras and Lie bialgebroids

  • Y. Kosmann-Schwarzbach

DOI: 10.1007/BF00996111

Cite this article as:
Kosmann-Schwarzbach, Y. Acta Appl Math (1995) 41: 153. doi:10.1007/BF00996111


We show that to any Poisson manifold and, more generally, to any triangular Lie bialgebroid in the sense of Mackenzie and Xu, there correspond two differential Gerstenhaber algebras in duality, one of which is canonically equipped with an operator generating the graded Lie algebra bracket, i.e. with the structure of a Batalin-Vilkovisky algebra.

Mathematics subject classifications (1991)

17B70 17B81 17B66 53C15 58F05 

Key words

Poisson manifolds Lie algebroids Lie bialgebroids Lie pseudo-algebras Schouten brackets graded Lie algebras Gerstenhaber algebras Batalin-Vilkovisky algebras topological field theories string theory 

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Y. Kosmann-Schwarzbach
    • 1
  1. 1.Centre de MathématiquesURA 169 du CNRS, Ecole PolytechniquePalaiseau CedexFrance

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