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On the Lie-formality of Poisson manifolds

Published online by Cambridge University Press:  04 March 2008

G. Sharygin  and
D. Talalaev
G. Sharygin
Affiliation:
sharygin@itep.ruInstitute for Theoretical and Experimental PhysicsITEP, 25 B. Cheremushkinskaya, Moscow, 117259, Russia
D. Talalaev
Affiliation:
talalaev@itep.ruInstitute for Theoretical and Experimental Physics, ITEP, 25 B. Cheremushkinskaya, Moscow, 117259, Russia
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Abstract

In the present note we prove formality of the differential graded Lie algebra of de Rham forms on a smooth Poisson manifold.

Keywords

Poisson manifoldBrylinski complexL∞-algebraL∞-morphism

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References

1.Kontsevich, M., Deformation quantization of Poisson manifolds, I, preprint arXiv:qalg/9709040Google Scholar
2.Penkava, M., Weldon, L., Infinity algebras, Massey products and deformations, preprint arXiv:math.QA/9808058Google Scholar
3.Sweedler, M. E., Hopf Algebras, W. A. Benjamin, New-York, 1969Google Scholar