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The Resource Algebraic Operads, by Jean-Louis Loday, Bruno Vallette, (electronic resource)

Algebraic Operads, by Jean-Louis Loday, Bruno Vallette, (electronic resource)

Creator
Author
Contributor
Summary
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 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 HomotopyTransfer Theorem. Although the necessary notions of algebra are recalled, readers areexpected 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 an elementary chapter on classical algebra, accessible to 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.
Language
  • eng
  • eng
Work
Publication
Edition
1st ed. 2012.
Extent
1 online resource (648 p.)
Note
Description based upon print version of record
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
Isbn
9781283630221
Instance
Label
Algebraic Operads
Title
Algebraic Operads
Statement of responsibility
by Jean-Louis Loday, Bruno Vallette
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
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 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 HomotopyTransfer Theorem. Although the necessary notions of algebra are recalled, readers areexpected 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 an elementary chapter on classical algebra, accessible to 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.
Member of
http://library.link/vocab/creatorName
Loday, Jean-Louis
Dewey number
516.3
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • q5QTXocZv_Q
  • s9nr_Z-7xmM
Language note
English
LC call number
QA169
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Vallette, Bruno.
Series statement
  • Grundlehren der mathematischen Wissenschaften,
  • Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
Series volume
  • 346
  • 346
http://library.link/vocab/subjectName
  • Algebra
  • Algebraic topology
  • Cell aggregation
  • Category Theory, Homological Algebra
  • Non-associative Rings and Algebras
  • Algebraic Topology
  • Manifolds and Cell Complexes (incl. Diff.Topology)
Label
Algebraic Operads, by Jean-Louis Loday, Bruno Vallette, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 609-623) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
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
Dimensions
unknown
Edition
1st ed. 2012.
Extent
1 online resource (648 p.)
Form of item
online
Isbn
9781283630221
Media category
computer
Media type code
c
Other control number
10.1007/978-3-642-30362-3
Specific material designation
remote
System control number
  • (CKB)2560000000090966
  • (EBL)1030212
  • (OCoLC)806458693
  • (SSID)ssj0000740466
  • (PQKBManifestationID)11480020
  • (PQKBTitleCode)TC0000740466
  • (PQKBWorkID)10699792
  • (PQKB)11223632
  • (DE-He213)978-3-642-30362-3
  • (MiAaPQ)EBC1030212
  • (EXLCZ)992560000000090966
Label
Algebraic Operads, by Jean-Louis Loday, Bruno Vallette, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 609-623) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
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
Dimensions
unknown
Edition
1st ed. 2012.
Extent
1 online resource (648 p.)
Form of item
online
Isbn
9781283630221
Media category
computer
Media type code
c
Other control number
10.1007/978-3-642-30362-3
Specific material designation
remote
System control number
  • (CKB)2560000000090966
  • (EBL)1030212
  • (OCoLC)806458693
  • (SSID)ssj0000740466
  • (PQKBManifestationID)11480020
  • (PQKBTitleCode)TC0000740466
  • (PQKBWorkID)10699792
  • (PQKB)11223632
  • (DE-He213)978-3-642-30362-3
  • (MiAaPQ)EBC1030212
  • (EXLCZ)992560000000090966

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