Softcover ISBN:  9780821805138 
Product Code:  CONM/202 
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Electronic ISBN:  9780821877937 
Product Code:  CONM/202.E 
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Book DetailsContemporary MathematicsVolume: 202; 1997; 443 ppMSC: Primary 08; 17; Secondary 16; 18; 55; 81;
“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.ReadershipGraduate students, research mathematicians, mathematical physicists, and physicists interested in general algebraic systems.

Table of Contents

Articles

J. P. May  Definitions: operads, algebras and modules [ MR 1436912 ]

Jim Stasheff  The prehistory of operads [ MR 1436913 ]

J. P. May  Operads, algebras and modules [ MR 1436914 ]

Andy Tonks  Relating the associahedron and the permutohedron [ MR 1436915 ]

Clemens Berger  Combinatorial models for real configuration spaces and $E_n$operads [ MR 1436916 ]

Jim Stasheff  From operads to “physically” inspired theories [ MR 1436917 ]

Allahtan Victor Gnedbaye  Opérades des algèbres $(k+1)$aires [ MR 1436918 ]

JeanMichel Oudom  Coproduct and cogroups in the category of graded dual Leibniz algebras [ MR 1436919 ]

HansJoachim Baues, Mamuka Jibladze and Andy Tonks  Cohomology of monoids in monoidal categories [ MR 1436920 ]

Thomas F. Fox and Martin Markl  Distributive laws, bialgebras, and cohomology [ MR 1436921 ]

David Balavoine  Deformations of algebras over a quadratic operad [ MR 1436922 ]

Terrence P. Bisson and André Joyal  $Q$rings and the homology of the symmetric groups [ MR 1436923 ]

J. P. May  Operadic tensor products and smash products [ MR 1436924 ]

Takashi Kimura, Alexander A. Voronov and Gregg J. Zuckerman  Homotopy Gerstenhaber algebras and topological field theory [ MR 1436925 ]

YiZhi Huang  Intertwining operator algebras, genuszero modular functors and genuszero conformal field theories [ MR 1436926 ]

Boris Feigin and Feodor Malikov  Modular functor and representation theory of $\widehat {\rm sl}_2$ at a rational level [ MR 1436927 ]

Jack Morava  Quantum generalized cohomology [ MR 1436928 ]

J.L. Brylinski and D. A. McLaughlin  Noncommutative reciprocity laws associated to finite groups [ MR 1436929 ]


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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 “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.

Articles

J. P. May  Definitions: operads, algebras and modules [ MR 1436912 ]

Jim Stasheff  The prehistory of operads [ MR 1436913 ]

J. P. May  Operads, algebras and modules [ MR 1436914 ]

Andy Tonks  Relating the associahedron and the permutohedron [ MR 1436915 ]

Clemens Berger  Combinatorial models for real configuration spaces and $E_n$operads [ MR 1436916 ]

Jim Stasheff  From operads to “physically” inspired theories [ MR 1436917 ]

Allahtan Victor Gnedbaye  Opérades des algèbres $(k+1)$aires [ MR 1436918 ]

JeanMichel Oudom  Coproduct and cogroups in the category of graded dual Leibniz algebras [ MR 1436919 ]

HansJoachim Baues, Mamuka Jibladze and Andy Tonks  Cohomology of monoids in monoidal categories [ MR 1436920 ]

Thomas F. Fox and Martin Markl  Distributive laws, bialgebras, and cohomology [ MR 1436921 ]

David Balavoine  Deformations of algebras over a quadratic operad [ MR 1436922 ]

Terrence P. Bisson and André Joyal  $Q$rings and the homology of the symmetric groups [ MR 1436923 ]

J. P. May  Operadic tensor products and smash products [ MR 1436924 ]

Takashi Kimura, Alexander A. Voronov and Gregg J. Zuckerman  Homotopy Gerstenhaber algebras and topological field theory [ MR 1436925 ]

YiZhi Huang  Intertwining operator algebras, genuszero modular functors and genuszero conformal field theories [ MR 1436926 ]

Boris Feigin and Feodor Malikov  Modular functor and representation theory of $\widehat {\rm sl}_2$ at a rational level [ MR 1436927 ]

Jack Morava  Quantum generalized cohomology [ MR 1436928 ]

J.L. Brylinski and D. A. McLaughlin  Noncommutative reciprocity laws associated to finite groups [ MR 1436929 ]