Geodesic
Homotopy BV algebras in Poisson geometry
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 74 (2013) no. 2, pp. 265-277.

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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 $\Delta(e^\xi)=e^\xi\left(\Delta(\xi)+\frac12[\xi,\xi]\right)$ 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. References: 17 entries. 
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C. Braun; A. Lazarev. Homotopy BV algebras in Poisson geometry. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 74 (2013) no. 2, pp. 265-277. http://geodesic.mathdoc.fr/item/MMO_2013_74_2_a3/

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