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Modules over Operads and Functors (Paperback, 2009 ed.)
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Modules over Operads and Functors (Paperback, 2009 ed.)
Series: Lecture Notes in Mathematics, 1967
Expected to ship within 18 - 22 working days
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The notion of an operad was introduced 40 years ago in algebraic
topology in order to model the structure of iterated loop spaces
[6, 47, 60]. Since then, operads have been used fruitfully in many
?elds of mathematics and physics. Indeed, the notion of an operad
supplies both a conceptual and e?ective device to handle a variety
of algebraic structures in various situations. Many
usualcategoriesofalgebras(likethecategoryofcommutativeandassociative
algebras, the category of associative algebras, the category of Lie
algebras, thecategoryofPoissonalgebras,...)areassociatedtooperads.
The main successful applications of operads in algebra occur in
defor- tion theory: the theory of operads uni?es the construction
of deformation complexes, gives generalizations of powerful methods
of rational homotopy, and brings to light deep connections between
the cohomology of algebras, the structure of combinatorial
polyhedra, the geometry of moduli spaces of surfaces, and conformal
?eld theory. The new proofs of the existence of
deformation-quantizations by Kontsevich and Tamarkin bring together
all these developments and lead Kontsevich to the fascinating
conjecture that the motivic Galois group operates on the space of
deformation-quantizations (see [35]). The purpose of this monograph
is to study not operads themselves, but modules over operads as a
device to model functors between categories of algebras as
e?ectively as operads model categories of algebras. Modules
overoperads occur naturally when one needs to representuniv- sal
complexes associated to algebras over operads (see [14, 54]).
Modules overoperads havenot been studied as extensively as operads
yet.
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