Modules over Operads and Functors
The notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. Operads were introduced 40 years ago in algebraic topology in order to model the structure of iterated loop spaces.
- PDF / 2,514,979 Bytes
- 304 Pages / 439.37 x 666.142 pts Page_size
- 50 Downloads / 273 Views
1967
Benoit Fresse
Modules over Operads and Functors
ABC
Benoit Fresse UFR de Mathématiques Université des Sciences et Technologies de Lille Cité Scientifique - Bâtiment M2 59655 Villeneuve d’Ascq Cedex France [email protected]
ISBN: 978-3-540-89055-3 DOI: 10.1007/978-3-540-89056-0
e-ISBN: 978-3-540-89056-0
Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2008938192 Mathematics Subject Classification (2000): Primary: 18D50; Secondary: 55P48, 18G55, 18A25 c Springer-Verlag Berlin Heidelberg 2009 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm 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. Violations are liable to prosecution under the German Copyright Law. 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. Cover design: SPi Publisher Services Printed on acid-free paper 987654321 springer.com
Preface
The notion of an operad was introduced 40 years ago in algebraic topology in order to model the structure of iterated loop spaces [6, 47, 60]. Since then, operads have been used fruitfully in many fields of mathematics and physics. Indeed, the notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. Many usual categories of algebras (like the category of commutative and associative algebras, the category of associative algebras, the category of Lie algebras, the category of Poisson algebras, . . . ) are associated to operads. The main successful applications of operads in algebra occur in deformation theory: the theory of operads unifies the construction of deformation complexes, gives generalizations of powerful methods of rational homotopy, and brings to light deep connections between the cohomology of algebras, the structure of combinatorial polyhedra, the geometry of moduli spaces of surfaces, and conformal field theory. The new proofs of the existence of deformation-quantizations by Kontsevich and Tamarkin bring together all these developments and lead Kontsevich to the fascinating conjecture that the motivic Galois group operates on the space of deformation-quantizations (see [35]). The purpose of this monograph is to study not operads themselves, but modules over operads as a device to model functors between categories of algebras as effectively as operads model categories of algebras. Modules over operads oc
Data Loading...
