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### Synopses & Reviews

#### Publisher Comments

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

### About the Author

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.

### Table of Contents

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
- Binding:
- Hardcover
- Publication date:
- 08/07/2012
- Publisher:
- Springer
- Language:
- English
- Pages:
- 636
- Height:
- 1.38IN
- Width:
- 6.14IN
- Series:
- Die Grundlehren der mathematischen Wissenschaften
- Series Number:
- 346
- Number of Units:
- 1
- Copyright Year:
- 2012
- Series Volume:
- 346
- Author:
- Author:
- Media Run Time:
- B
- Subject:
- 18D50, 17AXX, 18G50, 55P48, 57T30
- Subject:
- Mathematics
- Subject:
- mathematics and statistics
- Subject:
- Manifolds and Cell Complexes (incl. Diff.Topology)
- Subject:
- Non-associative Rings and Algebras
- Subject:
- twisting morphism
- Subject:
- Cell aggregation_xMathematics
- Subject:
- Category Theory, Homological Algebra
- Subject:
- Algebraic topology
- Subject:
- homotopical algebra
- Subject:
- B
- Subject:
- Algebra
- Subject:
- higher algebra
- Subject:
- Operad
- Subject:
- Koszul duality
- Subject:
- Mathematics-Abstract Algebra