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arXiv · 1304.6373

Homotopy BV algebras in Poisson geometry

Christopher Braun·Andrey Lazarev
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Abstract

We define and study the degeneration property for BV-infinity algebras and show that it implies that the underlying L-infinity algebras are homotopy abelian. The proof is based on a generalisation of the well-known identity Δ(e^x)=e^x(Δ(x)+[x,x]/2) which holds in all BV algebras. As an application we show that the higher Koszul brackets on the cohomology of a manifold supplied with a generalised Poisson structure all vanish.

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Christopher Braun, Andrey Lazarev. 2013-09-12. Homotopy BV algebras in Poisson geometry. https://doi.org/10.1090/s0077-1554-2014-00216-8

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