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
burgunder@math.univ-montp2.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 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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