Homotopy BV algebras in Poisson geometry. (English) Zbl 1306.53068
Trans. Mosc. Math. Soc. 2013, 217-227 (2013) and Tr. Mosk. Mat. O.-va 74, No. 2, 265-277 (2013).
A Batalin-Vilkovisky algebra is a graded commutative algebra supplied with an odd differential operator of order 2 and square zero. In this paper, the authors study the degeneration property for such algebras. It is proved that the underlying algebras are homotopy abelian. The proof is based on a generalization of a well-known identity for ordinary BV algebras. As an application, the authors show that the higher Koszul brackets on the cohomology of a manifold supplied with a generalized Poisson structure all vanish.
Reviewer: Angela Gammella-Mathieu (Metz)
MSC:
| 53D17 | Poisson manifolds; Poisson groupoids and algebroids |
| 16E45 | Differential graded algebras and applications (associative algebraic aspects) |
Keywords:
\(L_\infty\) algebra; BV algebra; Poisson manifold; differential operator; Koszul brackets; cohomologyReferences:
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