Ebook: Dialgebras and Related Operads

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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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.
Content:
Front Matter....Pages 1-5
Introduction....Pages 1-6
Dialgebras....Pages 7-66
Dialgebra (co)homology with coefficients....Pages 67-103
Un endofoncteur de la cat?gorie des op?rades....Pages 105-110
Un th?or?me de Milnor-Moore pour les alg?bres de Leibniz....Pages 111-133

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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.
Content:
Front Matter....Pages 1-5
Introduction....Pages 1-6
Dialgebras....Pages 7-66
Dialgebra (co)homology with coefficients....Pages 67-103
Un endofoncteur de la cat?gorie des op?rades....Pages 105-110
Un th?or?me de Milnor-Moore pour les alg?bres de Leibniz....Pages 111-133
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