Higher symplectic structure on torsionless Lie-Rinehart pairs

Mirco Richter

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arXiv · 1312.7752

Higher symplectic structure on torsionless Lie-Rinehart pairs

Mirco Richter

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Abstract

We define an n-plectic structure as a commutative and torsionless Lie Rinehart pair, together with a distinguished cocycle from its Chevalley-Eilenberg complex. This 'n-plectic cocycle' gives rise to an extension of the Chevalley-Eilenberg complex by so called symplectic tensors. The cohomology of this extension generalizes Hamiltonian functions and vector fields to tensors and cotensors in a range of degrees, up to certain coboundaries and has the structure of a Lie oo-algebra. Finally we show, that momentum maps appear in this context just as weak Lie oo-morphisms from an arbitrary Lie oo-algebra into the Lie oo-algebra of Hamiltonian (co)tensors.

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Mirco Richter. 2013-12-30. Higher symplectic structure on torsionless Lie-Rinehart pairs. https://arxiv.org/abs/1312.7752

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