A symmetric version of Kontsevich graph complex and Leibniz homology

Details A symmetric version of Kontsevich graph complex and Leibniz homology A symmetric version of Kontsevich graph complex and Leibniz homology

2008-04-13

arxiv.org/abs/0804.2052v1

Mathematics

Quantum Algebra

Scientific paper

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.

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