Algebraic Operads

• Main Authors: Loday, Jean-Louis (Author), Vallette, Bruno (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
• Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 346
• Subjects: Mathematics.; Category theory (Mathematics).; Homological algebra.; Nonassociative rings.; Rings (Algebra).; Algebraic topology.; Manifolds (Mathematics).; Complex manifolds.; Category Theory, Homological Algebra.; Non-associative Rings and Algebras.; Algebraic Topology.; Manifolds and Cell Complexes (incl. Diff.Topology).

In many areas of mathematics some “higher operations” are arising. These have become so important that several research 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 operad theo...

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.