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Journal of Lie Theory 20 (2010), No. 1, 127--165
Copyright Heldermann Verlag 2010

A Symmetric Version of Kontsevich Graph Complex and Leibniz Homology

Emily Burgunder
Institut de Mathématiques et de Modélisation, Université de Montpellier, Place Eugène Bataillon, 34095 Montpellier, France

Kontsevich has proven that the Lie homology of the Lie algebra of symplectic vector fields can be computed in terms of the homology of a graph complex. We prove that the Leibniz homology of this Lie algebra can be computed in terms of the homology of a variant of the graph complex endowed with an action of the symmetric groups. The resulting isomorphism is shown to be a Zinbiel-associative bialgebra isomorphism.

Keywords: Kontsevich graph complex, Leibniz homology, graph homology, Zinbiel-associative bialgebras, co-invariant theory.

MSC: 16E40, 16W22, 05C90

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