
Journal of Lie Theory 20 (2010), No. 1, 127165 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 burgunder@math.univmontp2.fr 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 Zinbielassociative bialgebra isomorphism. Keywords: Kontsevich graph complex, Leibniz homology, graph homology, Zinbielassociative bialgebras, coinvariant theory. MSC: 16E40, 16W22, 05C90 [ Fulltextpdf (357 KB)] for subscribers only. 