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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)

   
 
 

 

Homotopy BV algebras in Poisson geometry


Authors: C. Braun and A. Lazarev
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 74 (2013), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2013, 217-227
MSC (2010): Primary 14D15, 16E45, 53D17
DOI: https://doi.org/10.1090/S0077-1554-2014-00216-8
Published electronically: April 9, 2014
MathSciNet review: 3235797
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

C. Braun
Affiliation: Centre for Mathematical Sciences, City University London, London, United Kingdom
Email: Christopher.Braun.1@city.ac.uk

A. Lazarev
Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster, United Kingdom
Email: a.lazarev@lancaster.ac.uk

DOI: https://doi.org/10.1090/S0077-1554-2014-00216-8
Keywords: $L_{\infty}$ algebra, BV algebra, Poisson manifold, differential operator
Published electronically: April 9, 2014
Additional Notes: This work was partially supported by EPSRC grants EP/J00877X/1 and EP/J008451/1.
The authors would like to thank the Isaac Newton Institute for their hospitality during this work.
Article copyright: © Copyright 2014 C. Braun, A. Lazarev

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