Dialgebras and Related Operads
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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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