Journal of Lie Theory

no. 1
A Symmetric Version of Kontsevich Graph Complex and Leibniz Homology
Journal of Lie Theory, Volume 20 (2010) no. 1, pp. 127-165
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.
DOI: 10.5802/jolt.590
Classification: 16E40, 16W22, 05C90
Keywords: Kontsevich graph complex, Leibniz homology, graph homology, Zinbiel-associative bialgebras, co-invariant theory 
@article{JOLT_2010_20_1_a8,
     author = {E. Burgunder},
     title = {A {Symmetric} {Version} of {Kontsevich} {Graph} {Complex} and {Leibniz} {Homology}},
     journal = {Journal of Lie Theory},
     pages = {127--165},
     year = {2010},
     volume = {20},
     number = {1},
     doi = {10.5802/jolt.590},
     zbl = {1197.17011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.590/}
}
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E. Burgunder. A Symmetric Version of Kontsevich Graph Complex and Leibniz Homology. Journal of Lie Theory, Volume 20 (2010) no. 1, pp. 127-165. doi: 10.5802/jolt.590

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