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# Grundlehren Der Mathematischen Wissenschaften #346: Algebraic Operads

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 Comment on this title and you could win free books!Synopses & Reviews Table of Contents ISBN13: 9783642303616 ISBN10: 3642303617 Condition: All Product Details

### Synopses & Reviews

In many areas of mathematics some "higher operations" are popping up. These have become so important that several projects refer to such expressions. Higher operations form new types of algebras. The key to understanding and comparing them, to creating invariants of their action is

#### Synopsis:

This book offers a comprehensive and systematic approach to algebraic operads. It features an emphasis on the Koszul duality theory and gives applications to homotopy algebra. Includes examples, exercises, figures, as well as helpful chapter summaries.

#### Synopsis:

In many areas of mathematics some "higher operations" are popping up. These have become so important that several projects refer to such expressions. Higher operations form new types of algebras. The key to understanding and comparing them, to creating invariants of their action is

Jean-Louis Loday has worked in algebraic K-theory, algebraic topology, noncommutative geometry and higher algebra. He is the author of "Cyclic Homology" a worldwide reference, published as volume 301 in the Grundleheren der mathematischen Wissenschadften. He is an editor of several mathematical journals and several Proceedings. He has organized six of the annual conferences "Operads 20xx" (starting in 2004). Bruno Vallette has worked on operads since his first years in mathematical research. He is the author of 10 research articles and a specialist of properads and of Batalin-Vilkovisky algebras. Loday and Vallette organized several summer schools and international conferences on the subject (France, China, Norway) and published the Proceedings of these conferences.

Preface.- 1.Algebras, coalgebras, homology.- 2.Twisting morphisms.- 3.Koszul duality for associative algebras.- 4.Methods to prove Koszulity of an algebra.- 5.Algebraic operad.- 6 Operadic homological algebra.- 7.Koszul duality of operads.- 8.Methods to prove Koszulity of an operad.- 9.The operads As and A\infty.- 10.Homotopy operadic algebras.- 11.Bar and cobar construction of an algebra over an operad.- 12.(Co)homology of algebras over an operad.- 13.Examples of algebraic operads.- Apendices: A.The symmetric group.- B.Categories.- C.Trees.- References.- Index.- List of Notation.

### Product Details

ISBN:
9783642303616
Author:
Publisher:
Springer
Author:
Author:
Location:
Berlin, Heidelberg
Subject:
Algebra - Abstract
Subject:
18D50, 17AXX, 18G50, 55P48, 57T30
Subject:
Koszul duality
Subject:
higher algebra
Subject:
homotopical algebra
Subject:
Subject:
twisting morphism
Subject:
Category Theory, Homological Algebra
Subject:
Non-associative Rings and Algebras
Subject:
Algebraic topology
Subject:
Manifolds and Cell Complexes (incl. Diff.Topology)
Subject:
Mathematics-Abstract Algebra
Subject:
Mathematics
Subject:
B
Subject:
mathematics and statistics
Subject:
Algebra
Subject:
Cell aggregation_xMathematics
Edition Description:
2012
Series:
Die Grundlehren der mathematischen Wissenschaften
Series Volume:
346
Publication Date:
20120818
Binding:
HARDCOVER
Language:
English
Pages:
660
Dimensions:
235 x 155 mm

### Related Subjects

Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Topology