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Algebraic Operads (Paperback)
Loot Price: R3,431
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Algebraic Operads (Paperback)
Series: Grundlehren der mathematischen Wissenschaften, 346
Expected to ship within 18 - 22 working days
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In many areas of mathematics some "higher operations" are arising.
These havebecome so important that several research projects refer
to such expressions. Higher operationsform new types of algebras.
The key to understanding and comparing them, to creating invariants
of their action is operad theory. This is a point of view that is
40 years old in algebraic topology, but the new trend is its
appearance in several other areas, such as algebraic geometry,
mathematical physics, differential geometry, and combinatorics. The
present volume is the first comprehensive and systematic approach
to algebraic operads. An operad is an algebraic device that serves
to study all kinds of algebras (associative, commutative, Lie,
Poisson, A-infinity, etc.) from a conceptual point of view. The
book presents this topic with an emphasis on Koszul duality theory.
After a modern treatment of Koszul duality for associative
algebras, the theory is extended to operads. Applications to
homotopy algebra are given, for instance the Homotopy Transfer
Theorem. Although the necessary notions of algebra are recalled,
readers are expected to be familiar with elementary homological
algebra. Each chapter ends with a helpful summary and exercises. A
full chapter is devoted to examples, and numerous figures are
included. After a low-level chapter on Algebra, accessible to
(advanced) undergraduate students, the level increases gradually
through the book. However, the authors have done their best to make
it suitable for graduate students: three appendices review the
basic results needed in order to understand the various chapters.
Since higher algebra is becoming essential in several research
areas like deformation theory, algebraic geometry, representation
theory, differential geometry, algebraic combinatorics, and
mathematical physics, the book can also be used as a reference work
by researchers.
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