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Lie algebras of symplectic derivations and cycles on the moduli spaces

Shigeyuki Morita

Geometry & Topology Monographs 13 (2008) 335–354

DOI: 10.2140/gtm.2008.13.335

arXiv: math/0608673
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.

Keywords

derivation, homology of Lie algebras, moduli space of curves,
Mathematical Subject Classification

Primary: 17B40

Secondary: 17B56, 32G15
References
Publication

Received: 21 August 2006
Revised: 28 March 2007
Accepted: 30 March 2007
Published: 25 February 2008
Authors
Shigeyuki Morita
Graduate School of Mathematical Sciences
University of Tokyo
Komaba, Tokyo 153-8914
Japan