**Contemporary Mathematics**

Volume: 202;
1997;
443 pp;
Softcover

MSC: Primary 08; 17;
Secondary 16; 18; 55; 81

Print ISBN: 978-0-8218-0513-8

Product Code: CONM/202

List Price: $105.00

Individual Member Price: $84.00

**Electronic ISBN: 978-0-8218-7793-7
Product Code: CONM/202.E**

List Price: $105.00

Individual Member Price: $84.00

# Operads: Proceedings of Renaissance Conferences

Share this page *Edited by *
*Jean-Louis Loday; James D. Stasheff; Alexander A. Voronov*

“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 “Opérades et Algèbre Homotopique” held at the Centre International de Rencontres Mathématiques 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.

#### Table of Contents

# Table of Contents

## Operads: Proceedings of Renaissance Conferences

- Contents vii8 free
- Preface ix10 free
- Definitions: operads, algebras and modules 112 free
- The pre-history of operads 920
- Operads, algebras, and modules 1526
- Relating the associahedron and the permutohedron 3344
- Combinatorial models for real configuration spaces and En-operads 3748
- From operads to 'physically' inspired theories 5364
- Operades des algebres ( k + 1 )-aires 8394
- Coproduct and cogroups in the category of graded dual Leibniz algebras 115126
- Cohomology of monoids in monoidal categories 137148
- Distributive laws, bialgebras, and cohomology 167178
- Deformations of algebras over a quadratic operad 207218
- Q-rings and the homology of the symmetric groups 235246
- Operadic tensor products and smash products 287298
- Homotopy Gerstenhaber algebras and topological field theory 305316
- Intertwining operator algebras, genus-zero modular functors, and genus-zero conformal field theories 335346
- Modular functor and representation theory of sl2 at a rational level 357368
- Quantum generalized cohomology 407418
- Non-commutative reciprocity laws associated to finite groups 421432
- Index 439450 free

#### Readership

Graduate students, research mathematicians, mathematical physicists, and physicists interested in general algebraic systems.