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Lie algebras of symplectic derivations and cycles on the moduli spaces

Shigeyuki Morita
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Abstract

We consider the Lie algebra consisting of all derivations on the free associative algebra, generated by the first homology group of a closed oriented surface, which kill the symplectic class. We find the first non-trivial abelianization of this Lie algebra and discuss its relation to unstable cohomology classes of the moduli space of curves via a theorem of Kontsevich.

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Shigeyuki Morita. 2009-04-06. Lie algebras of symplectic derivations and cycles on the moduli spaces. https://doi.org/10.2140/gtm.2008.13.335

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