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E-book
Author Buan, Aslak Bakke

Title Algebras, Quivers and Representations : the Abel Symposium 2011
Published Dordrecht : Springer, 2013
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Description 1 online resource (311 pages)
Series Abel Symposia ; v. 8
Abel symposia.
Contents Algebras, Quivers and Representations; Foreword; Preface; Contents; Contributors; Preprojective Algebras, Singularity Categories and Orthogonal Decompositions; 1 Introduction; 1.1 Notation; 2 d-Representation Infinite Algebras and Preprojective Algebras; 3 The Singularity Category of a Gorenstein Algebra; 4 Orlov's Orthogonal Decomposition; 5 Examples; References; (Contravariant) Koszul Duality for DG Algebras; 1 Introduction; 2 Cup Products and Cap Products; 2.1 Notation; 2.2 Cup products; 2.3 Cap Products; 2.4 Opposite Cup Products; 2.5 Opposite Cap Products; 2.6 Morphisms; 2.7 Adjunction
Notes3 Twisted Tensor Products; 3.1 Notation; 3.2 Twisted Tensor Products; 3.3 Associativity; 3.4 Adjointness; 3.5 Naturality; 4 Acyclic Twisting Maps; 4.1 Notation; 4.2 Comparison Maps; 4.3 Acyclicity; 4.4 Bar Construction; 4.5 Cobar Construction; 4.6 (Co)augmentations; 4.7 Natural Resolutions; 4.8 Naturality; Notes; 5 Duals of DG Coalgebras; 5.1 Notation; 5.2 Duality; 5.3 Actions on Tensor Products; 6 Duals of Twisting Maps; 6.1 Notation; 6.2 Duality; 6.3 Actions on Duals; 7 Moore Duality; 7.1 Notation; 7.2 Semifree Resolutions; 7.3 Derived Category of DG Modules; 7.4 Subcategories
8 Composition Products8.1 Notation; 8.2 Morphisms; 8.3 Formal DG Algebras; 8.4 Derived Homomorphism Functors; 8.5 Naturality; 8.6 Controlled Resolutions; 9 Koszul Duality; 9.1 Augmented Models; 9.2 Homomorphisms of Comodules; Notes; 10 Koszul Algebras; 10.1 Notation; 10.2 Two-Homogeneity; 10.3 Quadratic Dual; 10.4 Priddy Construction; 10.5 Koszul Construction; Notes; 11 Golod DG Algebras; 11.1 Trivial Massey Operations; 11.2 Trivial Extensions; Notes; Appendix A: Complexes; A.1 Complexes; A.2 Homomorphisms; A.3 Tensor Products; A.4 Dual Complexes; Appendix B: DG Modules; B.1 DG Algebras
B.2 AugmentationsB. 3 Tensor Algebras; B.4 Left DG Modules; B.5 Right DG Modules; B.6 Semifree DG Modules; B.7 Left DG Bimodules; B.8 Twisters; Appendix C: DG Comodules; C.1 DG Coalgebras; C.2 Coaugmentations; C.3 Tensor Coalgebras; C.4 Left DG Comodules; C.5 Right DG Comodules; References; The Fundamental Group of a Morphism in a Triangulated Category; 1 Introduction; 2 The Fundamental Group of a Morphism; 2.1 Notation; 2.2 Triangulated Categories; 2.3 Turning Triangles; 2.4 Mattresses; 2.5 The Fundamental Groupoid; 2.6 The Outer Fundamental Group; 3 The Fundamental Group of an Extension
3.1 Exact Sequences Versus Triangles3.2 Extensions as Morphisms; 3.3 The Fundamental Groups of a Category; 3.4 The Case of 1-Extensions; References; On Hochschild Cohomology for Selfinjective Special Biserial Algebras; 1 Introduction; 2 Preliminaries; 2.1 The Algebras; 2.1.1 Hypothesis; Notation; 2.1.2 A Non-degenerate Bilinear Form; 2.2 A-Modules; 2.3 The First Few Bimodule Syzygies; 3 The Bimodule 1Agamma; 4 The Exact Sequence of Bimodules; 4.1 Periodicity of U; 5 Some Examples; 5.1 The Algebras with a2=0=b2; 5.1.1 The Module U; 5.1.2 The Case m+2-1 modulo n; 5.1.3 The Case m+20 modulo n
Summary This book features survey and research papers from The Abel Symposium 2011: Algebras, quivers and representations, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like, commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in repre
Notes 5.1.4 The Other Summand of U
Bibliography Includes bibliographical references
Notes Print version record
Subject Algebra -- Congresses.
Genre/Form Conference papers and proceedings.
Conference papers and proceedings.
Form Electronic book
Author Reiten, Idun, 1942-
Solberg, √ėyvind, 1961-
ISBN 3642394841 (hard cover ;) (alk. paper)
364239485X
9783642394843 (hard cover ;) (alk. paper)
9783642394850