TY - JOUR

T1 - Homotopy BV algebras in Poisson geometry

AU - Braun, Christopher

AU - Lazarev, Andrey

N1 - First published in Tranactions of the Moscow Mathematical Society in 74, 2, 2013, published by the American Mathematical Society

PY - 2013

Y1 - 2013

N2 - 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

AB - 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

KW - $L_{\infty}$ algebra

KW - BV algebra

KW - Poisson manifold

KW - differential operator

U2 - 10.1090/S0077-1554-2014-00216-8

DO - 10.1090/S0077-1554-2014-00216-8

M3 - Journal article

VL - 74

SP - 217

EP - 227

JO - Transactions of Moscow Mathematical Society

JF - Transactions of Moscow Mathematical Society

SN - 0077-1554

IS - 2

ER -