Dialgebras and Related Operads

Jean-Louis Loday, Frédéric Chapoton, Alessandra Frabetti, François Goichot (auth.)9783540421948, 3540421947

The main object of study of these four papers is the notion of associative dialgebras which are algebras equipped with two associative operations satisfying some more relations of the associative type. This notion is studied from a) the homological point of view: construction of the (co)homology theory with trivial coefficients and general coefficients, b) the operadic point of view: determination of the dual operad, that is the dendriform dialgebras which are strongly related with the planar binary trees, c) the algebraic point of view: Hopf structure and Milnor-Moore type theorem.

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Table of contents :
Introduction….Pages 1-6
Dialgebras….Pages 7-66
Dialgebra (co)homology with coefficients….Pages 67-103
Un endofoncteur de la catégorie des opérades….Pages 105-110
Un théoréme de Milnor-Moore pour les algèbres de Leibniz….Pages 111-133