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The Resource Algebraic Operads, by JeanLouis Loday, Bruno Vallette, (electronic resource)
Algebraic Operads, by JeanLouis Loday, Bruno Vallette, (electronic resource)
Resource Information
The item Algebraic Operads, by JeanLouis Loday, Bruno Vallette, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Algebraic Operads, by JeanLouis Loday, Bruno Vallette, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 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, Ainfinity, 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
 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
 Label
 Algebraic Operads
 Title
 Algebraic Operads
 Statement of responsibility
 by JeanLouis Loday, Bruno Vallette
 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, Ainfinity, 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.
 http://library.link/vocab/creatorName
 Loday, JeanLouis
 Dewey number
 516.3
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut

 q5QTXocZv_Q
 s9nr_Z7xmM
 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
 Nonassociative Rings and Algebras
 Algebraic Topology
 Manifolds and Cell Complexes (incl. Diff.Topology)
 Label
 Algebraic Operads, by JeanLouis Loday, Bruno Vallette, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. 609623) 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
 10.1007/9783642303623
 Specific material designation
 remote
 System control number

 (CKB)2560000000090966
 (EBL)1030212
 (OCoLC)806458693
 (SSID)ssj0000740466
 (PQKBManifestationID)11480020
 (PQKBTitleCode)TC0000740466
 (PQKBWorkID)10699792
 (PQKB)11223632
 (DEHe213)9783642303623
 (MiAaPQ)EBC1030212
 (EXLCZ)992560000000090966
 Label
 Algebraic Operads, by JeanLouis Loday, Bruno Vallette, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. 609623) 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
 10.1007/9783642303623
 Specific material designation
 remote
 System control number

 (CKB)2560000000090966
 (EBL)1030212
 (OCoLC)806458693
 (SSID)ssj0000740466
 (PQKBManifestationID)11480020
 (PQKBTitleCode)TC0000740466
 (PQKBWorkID)10699792
 (PQKB)11223632
 (DEHe213)9783642303623
 (MiAaPQ)EBC1030212
 (EXLCZ)992560000000090966
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.umanitoba.ca/portal/AlgebraicOperadsbyJeanLouisLodayBruno/d8WQw4zAV2E/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.umanitoba.ca/portal/AlgebraicOperadsbyJeanLouisLodayBruno/d8WQw4zAV2E/">Algebraic Operads, by JeanLouis Loday, Bruno Vallette, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.lib.umanitoba.ca/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.umanitoba.ca/">University of Manitoba Libraries</a></span></span></span></span></div>