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

[img]
Preview
PDF
1304.6373v2.pdf - Accepted Version

Download (211kB)

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
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
Subjects:
ID Code:
73429
Deposited By:
Deposited On:
18 Jun 2015 05:38
Refereed?:
Yes
Published?:
Published
Last Modified:
10 Apr 2020 02:23