Homotopy BV algebras in Poisson geometry

Braun, C.; Lazarev, A.

doi:10.1090/S0077-1554-2014-00216-8

Homotopy BV algebras in Poisson geometry
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by C. Braun and A. Lazarev

Trans. Moscow Math. Soc. 2013, 217-227

DOI: https://doi.org/10.1090/S0077-1554-2014-00216-8

Published electronically: April 9, 2014

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Abstract:

We define and study the degeneration property for $\mathrm {BV}_\infty$ algebras and show that it implies that the underlying $L_{\infty }$ algebras are homotopy abelian. The proof is based on a generalisation of the well-known identity $\Delta (e^{\xi })=e^{\xi }\Big (\Delta (\xi )+\frac {1}{2}[\xi ,\xi ]\Big )$ 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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