Quiver representations and quiver varieties:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2016]
|
| Series: | Graduate studies in mathematics
174 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xii, 295 Seiten Illustrationen, Diagramme |
| ISBN: | 9781470423070 |
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MARC
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| 245 | 1 | 0 | |a Quiver representations and quiver varieties |c Alexander Kirillov, Jr |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a xii, 295 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Graduate studies in mathematics |v 174 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Associative rings and algebras ... Representation theory of rings and algebras ... Representations of quivers and partially ordered sets |2 msc | |
| 650 | 7 | |a Algebraic geometry ... Cycles and subschemes ... Parametrization (Chow and Hilbert schemes) |2 msc | |
| 650 | 7 | |a Algebraic geometry ... Families, fibrations ... Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |2 msc | |
| 650 | 7 | |a Associative rings and algebras ... Representation theory of rings and algebras ... Representation type (finite, tame, wild, etc.) |2 msc | |
| 650 | 7 | |a Associative rings and algebras ... Representation theory of rings and algebras ... Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers |2 msc | |
| 650 | 7 | |a Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Representations, algebraic theory (weights) |2 msc | |
| 650 | 7 | |a Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Root systems |2 msc | |
| 650 | 7 | |a Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |2 msc | |
| 650 | 4 | |a Directed graphs | |
| 650 | 4 | |a Representations of graphs | |
| 650 | 4 | |a Graph theory | |
| 650 | 4 | |a Associative rings and algebras ... Representation theory of rings and algebras ... Representations of quivers and partially ordered sets | |
| 650 | 4 | |a Algebraic geometry ... Cycles and subschemes ... Parametrization (Chow and Hilbert schemes) | |
| 650 | 4 | |a Algebraic geometry ... Families, fibrations ... Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) | |
| 650 | 4 | |a Associative rings and algebras ... Representation theory of rings and algebras ... Representation type (finite, tame, wild, etc.) | |
| 650 | 4 | |a Associative rings and algebras ... Representation theory of rings and algebras ... Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers | |
| 650 | 4 | |a Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Representations, algebraic theory (weights) | |
| 650 | 4 | |a Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Root systems | |
| 650 | 4 | |a Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras | |
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Record in the Search Index
| _version_ | 1804176690176327680 |
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| adam_text | Titel: Quiver representations and quiver varieties
Autor: Kirillov, Alexander A
Jahr: 2016
Contents Preface xi Part 1. Dynkin Quivers Chapter 1. Basic Theory §1.1. Basic definitions §1.2. Path algebra; simple and indecomposable representations §1.3. ET-group and dimension §1.4. Projective modules and the standard resolution §1.5. Euler form §1.6. Dynkin and Euclidean graphs §1.7. Root lattice and Weyl group Chapter 2. Geometry of Orbits §2.1. Representation space §2.2. Properties of orbits §2.3. Closed orbits Chapter 3. Gabriel’s Theorem §3.1. Quivers of finite type §3.2. Reflection functors §3.3. Dynkin quivers §3.4. Coxeter element §3.5. Longest element and ordering of positive roots 3 3 7 11 11 15 16 20 23 23 24 26 31 31 32 38 41 43 Vll
Contents viii Chapter 4. Hall Algebras §4.1. Definition of Hall algebra §4.2. Serre relations and Ringel’s theorem §4.3. PBW basis §4.4. Hall algebra of constructible functions §4.5. Finite fields vs. complex numbers Chapter 5. Double Quivers §5.1. The double quiver §5.2. Preprojective algebra §5.3. Varieties A(v) §5.4. Composition algebra of the double quiver Part 2. Quivers of Infinite Type Chapter 6. Coxeter Functor and Preprojective Representations §6.1. Coxeter functor §6.2. Preprojective and preinjective representations §6.3. Auslander-Reiten quiver: Combinatorics §6.4. Auslander-Reiten quiver: Representation theory §6.5. Preprojective algebra and Auslander-Reiten quiver Chapter 7. Tame and Wild Quivers §7.1. Tame-wild dichotomy §7.2. Representations of the cyclic quiver §7.3. Affine root systems §7.4. Affine Coxeter element §7.5. Preprojective, preinjective, and regular representations §7.6. Category of regular representations §7.7. Representations of the Kronecker quiver §7.8. Classification of regular representations §7.9. Euclidean quivers are tame §7.10. Non-Euclidean quivers are wild §7.11. Kac’s theorem 47 47 52 56 61 66 69 69 70 72 75 83 84 86 88 92 96 103 103 105 106 107 112 113 118 121 126 127 129
Contents IX Chapter 8. McKay Correspondence and Representations of Euclidean Quivers 133 §8.1. Finite subgroups in SU(2) and regular polyhedra 133 §8.2. ADE classification of finite subgroups 135 §8.3. McKay correspondence 141 §8.4. Geometric construction of representations of Euclidean quivers 146 Part 3. Quiver Varieties Chapter 9. Hamiltonian Reduction and Geometric Invariant Theory 159 §9.1. Quotient spaces in differential geometry 159 §9.2. Overview of geometric invariant theory 160 §9.3. Relative invariants 163 §9.4. Regular points and resolution of singularities 168 §9.5. Basic definitions of symplectic geometry 171 §9.6. Hamiltonian actions and moment map 174 §9.7. Hamiltonian reduction 177 §9.8. Symplectic resolution of singularities and Springer resolution 180 §9.9. Kahler quotients 182 §9.10. Hyperkahler quotients 186 Chapter 10. Quiver Varieties 191 §10.1. GIT quotients for quiver representations 191 §10.2. GIT moduli spaces for double quivers 195 §10.3. Framed representations 200 §10.4. Framed representations of double quivers 204 §10.5. Stability conditions 206 §10.6. Quiver varieties as symplectic resolutions 210 §10.7. Example: Type A quivers and flag varieties 212 §10.8. Hyperkahler construction of quiver varieties 216 §10.9. C x action and exceptional fiber 219
X Contents Chapter 11. Jordan Quiver and Hilbert Schemes §11.1. Hilbert schemes §11.2. Quiver varieties for the Jordan quiver §11.3. Moduli space of torsion free sheaves §11.4. Anti-self-dual connections §11.5. Instantons on R 4 and ADHM construction Chapter 12. Kleinian Singularities and Geometric McKay Correspondence §12.1. Kleinian singularities §12.2. Resolution of Kleinian singularities via Hilbert schemes §12.3. Quiver varieties as resolutions of Kleinian singularities §12.4. Exceptional fiber and geometric McKay correspondence §12.5. Instantons on ALE spaces Chapter 13. Geometric Realization of Kac-Moody Lie Algebras §13.1. Borel-Moore homology §13.2. Convolution algebras §13.3. Steinberg varieties §13.4. Geometric realization of Kac-Moody Lie algebras Appendix A. Kac-Moody Algebras and Weyl Groups §A.l. Cartan matrices and root lattices §A.2. Weight lattice §A.3. Bilinear form and classification of Cartan matrices §A.4. Weyl group §A.5. Kac-Moody algebra §A.6. Root system §A.7. Reduced expressions §A.8. Universal enveloping algebra §A.9. Representations of Kac-Moody algebras Bibliography Index 225 225 227 230 235 238 241 241 243 245 248 253 259 259 261 264 266 273 273 274 275 276 277 278 280 281 282 285 293
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| id | DE-604.BV043829213 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:36:11Z |
| institution | BVB |
| isbn | 9781470423070 |
| language | English |
| lccn | 016018803 |
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| physical | xii, 295 Seiten Illustrationen, Diagramme |
| publishDate | 2016 |
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| publisher | American Mathematical Society |
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| spelling | Kirillov, Alexander Jr. 1967- Verfasser (DE-588)135930243 aut Quiver representations and quiver varieties Alexander Kirillov, Jr Providence, Rhode Island American Mathematical Society [2016] © 2016 xii, 295 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 174 Includes bibliographical references and index Associative rings and algebras ... Representation theory of rings and algebras ... Representations of quivers and partially ordered sets msc Algebraic geometry ... Cycles and subschemes ... Parametrization (Chow and Hilbert schemes) msc Algebraic geometry ... Families, fibrations ... Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) msc Associative rings and algebras ... Representation theory of rings and algebras ... Representation type (finite, tame, wild, etc.) msc Associative rings and algebras ... Representation theory of rings and algebras ... Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers msc Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Representations, algebraic theory (weights) msc Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Root systems msc Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras msc Directed graphs Representations of graphs Graph theory Associative rings and algebras ... Representation theory of rings and algebras ... Representations of quivers and partially ordered sets Algebraic geometry ... Cycles and subschemes ... Parametrization (Chow and Hilbert schemes) Algebraic geometry ... Families, fibrations ... Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) Associative rings and algebras ... Representation theory of rings and algebras ... Representation type (finite, tame, wild, etc.) Associative rings and algebras ... Representation theory of rings and algebras ... Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Representations, algebraic theory (weights) Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Root systems Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras Graduate studies in mathematics 174 (DE-604)BV009739289 174 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029240040&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kirillov, Alexander Jr. 1967- Quiver representations and quiver varieties Graduate studies in mathematics Associative rings and algebras ... Representation theory of rings and algebras ... Representations of quivers and partially ordered sets msc Algebraic geometry ... Cycles and subschemes ... Parametrization (Chow and Hilbert schemes) msc Algebraic geometry ... Families, fibrations ... Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) msc Associative rings and algebras ... Representation theory of rings and algebras ... Representation type (finite, tame, wild, etc.) msc Associative rings and algebras ... Representation theory of rings and algebras ... Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers msc Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Representations, algebraic theory (weights) msc Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Root systems msc Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras msc Directed graphs Representations of graphs Graph theory Associative rings and algebras ... Representation theory of rings and algebras ... Representations of quivers and partially ordered sets Algebraic geometry ... Cycles and subschemes ... Parametrization (Chow and Hilbert schemes) Algebraic geometry ... Families, fibrations ... Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) Associative rings and algebras ... Representation theory of rings and algebras ... Representation type (finite, tame, wild, etc.) Associative rings and algebras ... Representation theory of rings and algebras ... Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Representations, algebraic theory (weights) Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Root systems Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
| title | Quiver representations and quiver varieties |
| title_auth | Quiver representations and quiver varieties |
| title_exact_search | Quiver representations and quiver varieties |
| title_full | Quiver representations and quiver varieties Alexander Kirillov, Jr |
| title_fullStr | Quiver representations and quiver varieties Alexander Kirillov, Jr |
| title_full_unstemmed | Quiver representations and quiver varieties Alexander Kirillov, Jr |
| title_short | Quiver representations and quiver varieties |
| title_sort | quiver representations and quiver varieties |
| topic | Associative rings and algebras ... Representation theory of rings and algebras ... Representations of quivers and partially ordered sets msc Algebraic geometry ... Cycles and subschemes ... Parametrization (Chow and Hilbert schemes) msc Algebraic geometry ... Families, fibrations ... Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) msc Associative rings and algebras ... Representation theory of rings and algebras ... Representation type (finite, tame, wild, etc.) msc Associative rings and algebras ... Representation theory of rings and algebras ... Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers msc Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Representations, algebraic theory (weights) msc Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Root systems msc Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras msc Directed graphs Representations of graphs Graph theory Associative rings and algebras ... Representation theory of rings and algebras ... Representations of quivers and partially ordered sets Algebraic geometry ... Cycles and subschemes ... Parametrization (Chow and Hilbert schemes) Algebraic geometry ... Families, fibrations ... Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) Associative rings and algebras ... Representation theory of rings and algebras ... Representation type (finite, tame, wild, etc.) Associative rings and algebras ... Representation theory of rings and algebras ... Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Representations, algebraic theory (weights) Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Root systems Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
| topic_facet | Associative rings and algebras ... Representation theory of rings and algebras ... Representations of quivers and partially ordered sets Algebraic geometry ... Cycles and subschemes ... Parametrization (Chow and Hilbert schemes) Algebraic geometry ... Families, fibrations ... Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) Associative rings and algebras ... Representation theory of rings and algebras ... Representation type (finite, tame, wild, etc.) Associative rings and algebras ... Representation theory of rings and algebras ... Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Representations, algebraic theory (weights) Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Root systems Nonassociative rings and algebras ... Lie algebras and Lie superalgebras ... Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras Directed graphs Representations of graphs Graph theory |
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