Dialgebras and Related Operads
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		    1763
 
 3 Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo
 
 J.-L. Loday A. Frabetti F. Chapoton F. Goichot
 
 Dialgebras and Related Operads
 
 123
 
 Authors Jean-Louis Loday Institut de Recherche Mathématique Avancée CNRS et Université Louis Pasteur 7 rue R. Descartes 67084 Strasbourg Cedex, France
 
 Frédéric Chapoton Institut de Mathématiques de Jussieu Université Pierre et Marie Curie 175 rue du Chevaleret 75013 Paris, France E-mail: [email protected]
 
 E-mail: [email protected] Alessandra Frabetti Institut de Mathématiques Université de Lausanne 1015 Lausanne, Switzerland E-mail: [email protected]
 
 Franc¸ois Goichot Institut des Sciences et Techniques – Lamath Université de Valenciennes et du Hainaut Cambrésis Le Mont Houy 59313 Valenciennes Cedex 9, France E-mail: [email protected]
 
 Cataloging-in-Publication Data applied for
 
 Mathematics Subject Classification (2000): 05C5, 16A24, 16W30, 17Axx, 17D99, 18D50, 18G60, 55Uxx ISSN 0075-8434 ISBN 3-540-42194-7 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2001 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the authors SPIN: 10841327 41/3142/LK - 543210 - Printed on acid-free paper
 
 Table of contents
 
 Introduction
 
 ............................................................
 
 1
 
 Dialgebras Jean-Louis
 
 Loday
 
 .........................................................
 
 Dialgebra (co)homology Alessandra Frabetti
 
 with coefficients
 
 ......................................................
 
 Un endofoncteur de la categorie des Fr6d,6ric
 
 Chapoton
 
 67
 
 operades
 
 ......................................................
 
 Un theoreme de Milnor-Moore pour les Frangois Goichot
 
 7
 
 algebres,
 
 105
 
 de Leibniz
 
 .......................................................
 
 111
 
 Introduction
 
 The four common
 
 bras.
 
 The first
 
 algebraic
 
 in
 
 of this
 
 papers
 
 feature
 
 is to have
 
 dialgebras)
 
 It
 
 with
 
 deal
 
 generating
 
 to introduce
 
 motivation
 
 K-theory. closely
 
 volume
 
 two
 
 turned
 
 So
 
 operations.
 
 algebraic
 
 such
 
 later		
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