alexa DECOMPOSITION OF DENDRIFORM HOMOLOGY FOR ZINBIEL ALGEBRAS
Mathematics

Mathematics

Journal of Generalized Lie Theory and Applications

Author(s): Franois Goichot

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Zinbiel algebras are certain ("dendriform") asso ciative algebras, with a commutativity condition. We show that their homology, when con-sidered as dendriform algebras, splits into pieces, and the rst piece is their homology as Zinbiel algebras. This decomp osition is similar to the well-known splitting of Ho chschild homology of a commutative algebra, where the rst piece is Harrison homology. In fact, these two splittings are compatible, when the Zinbiel algebra is considered as a commutative one. This new decomp osition is obtained via "eulerian" idemp otents, which we construct by convolution, in an appropriate Hopf-dialgebra setting. We also consider the non-commutative case,where Pre-Lie algebras come in.

 

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This article was published in J. Pure and Applied Algebra and referenced in Journal of Generalized Lie Theory and Applications

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