泊松几何中的同伦BV代数

Q2 Mathematics

Transactions of the Moscow Mathematical Society Pub Date : 2013-04-23 DOI:10.1090/S0077-1554-2014-00216-8

Christopher Braun, A. Lazarev

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引用次数: 27

摘要

我们定义并研究了$ \mathrm {BV}_\infty $代数的退化性质，并证明了其隐含的$ L_{\infty }$代数是同伦阿贝尔的。这个证明是基于一个众所周知的恒等式$ \Delta (e^{\xi })=e^{\xi }\Big (\Delta (\xi )+\frac {1}{2}[\xi ,\xi ]\Big )$的推广，它适用于所有的BV代数。作为一个应用，我们证明了具有广义泊松结构的流形上同调上的高Koszul括号全部消失。-详见:http://www.ams.org/journals/mosc/2013-74-00/S0077-1554-2014-00216-8/＃sthash.pBIIcZKa.dpuf

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Homotopy BV algebras in Poisson geometry

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

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来源期刊

Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)

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期刊介绍： This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.