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Homotopy BV algebras in Poisson geometry

Authors
  • Braun, Christopher
  • Lazarev, Andrey
Type
Published Article
Publication Date
Sep 12, 2013
Submission Date
Apr 23, 2013
Identifiers
DOI: 10.1090/S0077-1554-2014-00216-8
Source
arXiv
License
Yellow
External links

Abstract

We define and study the degeneration property for BV-infinity algebras and show that it implies that the underlying L-infinity algebras are homotopy abelian. The proof is based on a generalisation of the well-known identity \Delta(e^x)=e^x(\Delta(x)+[x,x]/2) 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.

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