Algebraic Operads

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 o...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Loday, Jean-Louis (Autor), Vallette, Bruno (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
Edición:1st ed. 2012.
Colección:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 346
Temas:
Algebra, Homological.
Nonassociative rings.
Algebraic topology.
Manifolds (Mathematics).
Category Theory, Homological Algebra.
Non-associative Rings and Algebras.
Algebraic Topology.
Manifolds and Cell Complexes.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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