Dialgebras and related operads / J.-L. Loday [and others].
Contributor(s): Loday, Jean-LouisMaterial type: TextLanguage: English, French Series: Lecture notes in mathematics (Springer-Verlag): 1763.Publisher: Berlin ; New York : Springer, ©2001Description: 1 online resource (133 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540453284; 3540453288Subject(s): Algebra, Homological | Algebra, HomologicalGenre/Form: Electronic books. Additional physical formats: Print version:: Dialgebras and related operads.DDC classification: 510 s | 512/.55 LOC classification: QA3 | .L28 no. 1763 | QA169Online resources: Click here to access online
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Includes bibliographical references.
English and French.
Dialgebras / Jean-Louis Loday -- Dialgebra (co)homology with coefficients / Alessandra Frabetti -- Un endofoncteur de la catégorie des opérades / Frédéric Chapoton -- Un théorème de Milnor-Moore pour les algèbres de Leibniz / François Goichot.
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.