Modules over Operads and Functors

Language: English

Published by Springer Vieweg, Springer Mär 2009, 2009

3540890556 / 9783540890553

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This item is printed on demand - Print on Demand Titel. Neuware -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 elds of mathematics and physics. Indeed, the notion of an operad supplies both a conceptual and e ective device to handle a variety of algebraic structures in various situations. Many usualcategoriesofalgebras(likethecategoryofcommutativeandassociative algebras, the category of associative algebras, the category of Lie algebras, thecategoryofPoissonalgebras.)areassociatedtooperads. The main successful applications of operads in algebra occur in defor- tion theory: the theory of operads uni es 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 eld 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 e ectively as operads model categories of algebras. Modules overoperads occur naturally when one needs to representuniv- sal complexes associated to algebras over operads (see [14, 54]). Modules overoperads havenot been studied as extensively as operads yet.Springer-Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 324 pp. Englisch.

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Title
Modules over Operads and Functors
Author
Benoit Fresse
Publisher
Springer Vieweg, Springer Mär 2009
Publication year
2009
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3540890556
ISBN 13
9783540890553
Item weight
493 grams
Dimensions
235x155x18 mm

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