Operads : Proceedings of Renaissance Conferences

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'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

  • Paperback | 443 pages
  • 171.45 x 241.3 x 25.4mm | 771.11g
  • Providence, United States
  • English, French
  • 0821805134
  • 9780821805138

Table of contents

Definitions: operads, algebras, and modules by J. P. May The pre-history of operads by J. Stasheff Operads, algebras, and modules by J. P. May Relating the associahedron and the permutohedron by A. Tonks Combinatorial models for real configuration spaces and $E_n$-operads by C. Berger From operads to 'physically' inspired theories by J. Stasheff Operades des algebres $(k+1)$-aires by A. V. Gnedbaye Coproduct and cogroups in the category of graded dual Leibniz algebras by J.-M. Oudom Cohomology of monoids in monoidal categories by H.-J. Baues, M. Jibladze, and A. Tonks Distributive laws, bialgebras, and cohomology by T. F. Fox and M. Markl Deformations of algebras over a quadratic operad by D. Balavoine $Q$-rings and the homology of the symmetric groups by T. P. Bisson and A. Joyal Operadic tensor products and smash products by J. P. May Homotopy Gerstenhaber algebras and topological field theory by T. Kimura, A. A. Voronov, and G. J. Zuckerman Intertwining operator algebras, genus-zero modular functors, and genus-zero conformal field theories by Y.-Z. Huang Modular functor and representation theory of $\widehat {sl_2}$ at a rational level by B. Feigin and F. Malikov Quantum generalized cohomology by J. Morava Non-commutative reciprocity laws associated to finite groups by J.-L. Brylinski and D. A. McLaughlin.
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Review quote

We believe that the book will be useful to everybody interested in this exciting area of active research in which pure mathematics and mathematical physics interact. European Mathematical Society Newsletter
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