# Homotopy BV algebras in Poisson geometry

Braun, Christopher and Lazarev, Andrey (2013) Homotopy BV algebras in Poisson geometry. Transactions of Moscow Mathematical Society, 74 (2). pp. 217-227. ISSN 0077-1554

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1304.6373v2.pdf - Accepted Version

## 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. - See more at: http://www.ams.org/journals/mosc/2013-74-00/S0077-1554-2014-00216-8/#sthash.pBIIcZKa.dpuf

Item Type: Journal Article Transactions of Moscow Mathematical Society First published in Tranactions of the Moscow Mathematical Society in 74, 2, 2013, published by the American Mathematical Society Faculty of Science and Technology > Mathematics and Statistics 73429 ep_importer_pure 18 Jun 2015 05:38 Yes Published 18 Feb 2020 02:10 https://eprints.lancs.ac.uk/id/eprint/73429