Operads: Proceedings of Renaissance Conferences

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Brand new. We distribute directly for the publisher. "Operads" are mathematical devices which model many sorts of algebras (such as associative, commutative, Lie, Poisson, ... alternative, Leibniz, etc., including those defined up to homotopy, such as $A_{\infty}$-algebras). Since the notion of an operad appeared in the seventies in algebraic topology, there has been a renaissance of this theory due to the discovery of relationships with graph cohomology, Koszul duality, representation theory, combinatorics, cyclic cohomology, moduli spaces, knot theory, and quantum field theory.This renaissance was recognized at a special session "Moduli Spaces, Operads, and Representation Theory" of the AMS meeting in Hartford, CT (March 1995), and at a conference "Oprades et Algbre Homotopique" held at the Centre International de Rencontres Mathmatiques at Luminy, France (May-June 1995). Both meetings drew a diverse group of researchers.The authors have arranged the contributions so as to emphasize certain themes around which the renaissance of operads took place: homotopy algebra, algebraic topology, polyhedra and combinatorics, and applications to physics. Read more Show Less

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Overview

''Operads'' are mathematical devices which model many sorts of algebras (such as associative, commutative, Lie, Poisson, alternative, Leibniz, etc., including those defined up to homotopy, such as $A_{\infty}$-algebras). Since the notion of an operad appeared in the seventies in algebraic topology, there has been a renaissance of this theory due to the discovery of relationships with graph cohomology, Koszul duality, representation theory, combinatorics, cyclic cohomology, moduli spaces, knot theory, and quantum field theory. This renaissance was recognized at a special session ''Moduli Spaces, Operads, and Representation Theory'' of the AMS meeting in Hartford, CT (March 1995), and at a conference ''Operades et Algebre Homotopique'' held at the Centre International de Rencontres Mathematiques at Luminy, France (May-June 1995). Both meetings drew a diverse group of researchers. The authors have arranged the contributions so as to emphasize certain themes around which the renaissance of operads took place: homotopy algebra, algebraic topology, polyhedra and combinatorics, and applications to physics.

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Product Details

Table of Contents

Preface
Definitions: operads, algebras and modules 1
The pre-history of operads 9
Operads, algebras, and modules 15
Relating the associahedron and the permutohedron 33
Combinatorial models for real configuration spaces and E[subscript n]-operads 37
From operads to 'physically' inspired theories 53
Operades des algebres (k + 1)-aires 83
Coproduct and cogroups in the category of graded dual Leibniz algebras 115
Cohomology of monoids in monoidal categories 137
Distributive laws, bialgebras, and cohomology 167
Deformations of algebras over a quadratic operad 207
Q-rings and the homology of the symmetric groups 235
Operadic tensor products and smash products 287
Homotopy Gerstenhaber algebras and topological field theory 305
Intertwining operator algebras, genus-zero modular functors, and genus-zero conformal field theories 335
Modular functor and representation theory of [actual symbol not reproducible] at a rational level 357
Quantum generalized cohomology 407
Non-commutative reciprocity laws associated to finite groups 421
Index 439
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