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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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
Journal or Publication Title: Transactions of Moscow Mathematical Society
Additional Information: First published in Tranactions of the Moscow Mathematical Society in 74, 2, 2013, published by the American Mathematical Society
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 73429
Deposited By: ep_importer_pure
Deposited On: 18 Jun 2015 05:38
Refereed?: Yes
Published?: Published
Last Modified: 18 Feb 2020 02:10
URI: https://eprints.lancs.ac.uk/id/eprint/73429

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