Softcover ISBN:  9780821805138 
Product Code:  CONM/202 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821877937 
Product Code:  CONM/202.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821805138 
eBook: ISBN:  9780821877937 
Product Code:  CONM/202.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 
Softcover ISBN:  9780821805138 
Product Code:  CONM/202 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821877937 
Product Code:  CONM/202.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821805138 
eBook ISBN:  9780821877937 
Product Code:  CONM/202.B 
List Price:  $255.00 $192.50 
MAA Member Price:  $229.50 $173.25 
AMS Member Price:  $204.00 $154.00 

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 ]