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Edited by: Jean-Louis Loday, University of Strasbourg, France, James D. Stasheff, University of North Carolina, Chapel Hill, NC, and Alexander A. Voronov, CNRS, Université Louis Pasteur, Strasbourg, France
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Contemporary Mathematics
1997; 443 pp; softcover
Volume: 202
ISBN-10: 0-8218-0513-4
ISBN-13: 978-0-8218-0513-8
List Price: US$103 Member Price: US$82.40
Order Code: CONM/202

"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.

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

• J. P. May -- Definitions: operads, algebras, and modules
• J. Stasheff -- The pre-history of operads
• J. P. May -- Operads, algebras, and modules
• A. Tonks -- Relating the associahedron and the permutohedron
• C. Berger -- Combinatorial models for real configuration spaces and $$E_n$$-operads
• J. Stasheff -- From operads to `physically' inspired theories
• A. V. Gnedbaye -- Opérades des algèbres $$(k+1)$$-aires
• J.-M. Oudom -- Coproduct and cogroups in the category of graded dual Leibniz algebras
• H.-J. Baues, M. Jibladze, and A. Tonks -- Cohomology of monoids in monoidal categories
• T. F. Fox and M. Markl -- Distributive laws, bialgebras, and cohomology
• T. P. Bisson and A. Joyal -- $$Q$$-rings and the homology of the symmetric groups
• B. Feigin and F. Malikov -- Modular functor and representation theory of $$\widehat {sl_2}$$ at a rational level