tailieunhanh - Green Functors and G-sets~

The theory of Mackey functors has been developed during the last 25 years in a series of papers by various authors (. Green [8], a. Dress [5], T. Yoshida [17], J. Th~venaz and P. Webb [13],[15],[14], G. Lewis [6]). It is an attempt to give a single framework for the different theories of representations of a finite group and its subgroups. The notion of Mackey functor for a group G can be essentially approached from three points of view: the first one ([8]), which I call "naive", relics on the poset of subgroups of G. The second one ([5],[17]) is more "categoric", and relies on the category. | Serge Bouc Green Functors and G-sets Springer Author Serge Bouc Equipe des groupes finis CNRS UMR 9994 UFR de Mathématiques Université Paris 7 - Denis Diderot 2 Place Jussieu F-75251 Paris France e-mail bouc@. fr Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufhahme Bouc Serge Green functors and G-sets I Serge Bouc. - Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo Springer 1997 Lecture notes in mathematics 1671 ISBN 3-540-63550-5 Mathematics Subject Classification 1991 19A22 20C05 20J06 18D35 ISSN 0075-8434 ISBN 3-540-63550-5 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 1997 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 TpX output by the author SPIN 10553356 46 3142-543210 - Printed on acid-free paper Contents 1 Mackey functors 5 Equivalent definitions. 5 Definition in terms of subgroups. 5 Definition in terms of G-sets. 6 Definition as modules over the Mackey algebra. 7 The Mackey functors M 1 7 My. 8 Construction of H M N and M N. 9 Identification of H M N . 10 .