A journey through representation theory : from finite groups to Quivers via Algebras / Caroline Gruson y Vera Serganova
Series UniversitextEditor: Cham Springer 2018Edición: 1st edDescripción: 223 pages ; 24 cmISBN: 9783319982694Otra clasificación: 20-02 (16G20 16T05 20C30 20G05)Preface vii -- Chapter 1. Introduction to representation theory of finite groups [1] -- 1. Definitions and examples [1] -- 2. Ways to produce new representations [3] -- 3. Invariant subspaces and irreducibility [4] -- 4. Characters [7] -- 5. Examples [15] -- 6. Invariant forms [18] -- 7. Representations over R [21] -- 8. Relationship between representations over R and over C [22] -- Chapter 2. Modules with applications to finite groups [25] -- 1. Modules over associative rings [25] -- 2. Finitely generated modules and Noetherian rings [28] -- 3. The centre of the group algebra k (G) [30] -- 4. One application [33] -- 5. General facts on induced modules [34] -- 6. Induced representations for groups [36] -- 7. Double cosets and restriction to a subgroup [38] -- 8. Mackey’s criterion [40] -- 9. Hecke algebras, a first glimpse [41] -- 10. Some examples [42] -- 11. Some general facts about field extension [43] -- 12. Artin’s theorem and representations over Q [45] -- Chapter 3. Representations of compact groups [47] -- 1. Compact groups [47] -- 2. Orthogonality relations and Peter-Weyl Theorem [55] -- 3. Examples [58] -- Chapter 4. Results about unitary representations [65] -- 1. Unitary representations of Rn and Fourier transform [65] -- 2. Heisenberg groups and the Stone—von Neumann theorem70 -- 3. Representations of SL2 (R) [77] -- Chapter 5. On algebraic methods [81] -- 1. Introduction [81] -- 2. Semisimple modules and density theorem [81] -- 3. Wedderburn—Artin theorem [84] -- 4. Jordan-Holder theorem and indecomposable modules [85] -- 5. A bit of homological algebra [90] -- 6. Projective modules [93] -- 7. Representations of Artinian rings [99] -- 8. Abelian categories [103] -- Chapter 6. Symmetric groups, Schur—Weyl duality and positive self-adjoint Hopf algebras [105] -- 1. Representations of symmetric groups [105] -- 2. Schur—Weyl duality [110] -- 3. General facts on Hopf algebras [104] -- 4. The Hopf algebra associated to the representations of symmetric groups [117] -- 5. Classification of PSH algebras part 1: decomposition theorem [119] -- 6. Classification of PSH algebras part 2: unicity for the rank 1 case [121] -- 7. Bases of PSH algebras of rank one [125] -- 8. Harvest [131] -- 9. General linear groups over a finite field [138] -- Chapter 7. Introduction to representation theory of quivers [149] -- 1. Representations of quivers [149] -- 2. Path algebra [152] -- 3. Standard resolution and consequences [155] -- 4. Bricks [159] -- 5. Orbits in representation varieties [161] -- 6. Coxeter-Dynkin and affine graphs [163] -- 7. Quivers of finite type and Gabriel’s theorem [167] -- Chapter 8. Representations of Dynkin and affine quivers [169] -- 1. Reflection functors [169] -- 2. Reflection functors and change of orientation [172] -- 3. Weyl group and reflection functors [172] -- 4. Coxeter functors [173] -- 5. Further properties of Coxeter functors [174] -- 6. Affine root systems [177] -- 7 Preprojective and preiniective representations [179] -- 8. Regular representations [182] -- 9. Indecomposable representations of affine quivers [189] -- Chapter 9. Applications of quivers [193] -- 1. From abelian categories to algebras [193] -- 2. From categories to quivers [195] -- 3. Finitely represented, tame and wild algebras [199] -- 4. Frobenius algebras [200] -- 5. Application to group algebras [202] -- 6. On certain categories of -modules [205] -- Bibliography [219] -- Index [221] --
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | Últimas adquisiciones | 20 G892 (Browse shelf) | Available | A-9386 |
Preface vii --
Chapter 1. Introduction to representation theory of finite groups [1] --
1. Definitions and examples [1] --
2. Ways to produce new representations [3] --
3. Invariant subspaces and irreducibility [4] --
4. Characters [7] --
5. Examples [15] --
6. Invariant forms [18] --
7. Representations over R [21] --
8. Relationship between representations over R and over C [22] --
Chapter 2. Modules with applications to finite groups [25] --
1. Modules over associative rings [25] --
2. Finitely generated modules and Noetherian rings [28] --
3. The centre of the group algebra k (G) [30] --
4. One application [33] --
5. General facts on induced modules [34] --
6. Induced representations for groups [36] --
7. Double cosets and restriction to a subgroup [38] --
8. Mackey’s criterion [40] --
9. Hecke algebras, a first glimpse [41] --
10. Some examples [42] --
11. Some general facts about field extension [43] --
12. Artin’s theorem and representations over Q [45] --
Chapter 3. Representations of compact groups [47] --
1. Compact groups [47] --
2. Orthogonality relations and Peter-Weyl Theorem [55] --
3. Examples [58] --
Chapter 4. Results about unitary representations [65] --
1. Unitary representations of Rn and Fourier transform [65] --
2. Heisenberg groups and the Stone—von Neumann theorem70 --
3. Representations of SL2 (R) [77] --
Chapter 5. On algebraic methods [81] --
1. Introduction [81] --
2. Semisimple modules and density theorem [81] --
3. Wedderburn—Artin theorem [84] --
4. Jordan-Holder theorem and indecomposable modules [85] --
5. A bit of homological algebra [90] --
6. Projective modules [93] --
7. Representations of Artinian rings [99] --
8. Abelian categories [103] --
Chapter 6. Symmetric groups, Schur—Weyl duality and positive self-adjoint Hopf algebras [105] --
1. Representations of symmetric groups [105] --
2. Schur—Weyl duality [110] --
3. General facts on Hopf algebras [104] --
4. The Hopf algebra associated to the representations of symmetric groups [117] --
5. Classification of PSH algebras part 1: decomposition theorem [119] --
6. Classification of PSH algebras part 2: unicity for the rank 1 case [121] --
7. Bases of PSH algebras of rank one [125] --
8. Harvest [131] --
9. General linear groups over a finite field [138] --
Chapter 7. Introduction to representation theory of quivers [149] --
1. Representations of quivers [149] --
2. Path algebra [152] --
3. Standard resolution and consequences [155] --
4. Bricks [159] --
5. Orbits in representation varieties [161] --
6. Coxeter-Dynkin and affine graphs [163] --
7. Quivers of finite type and Gabriel’s theorem [167] --
Chapter 8. Representations of Dynkin and affine quivers [169] --
1. Reflection functors [169] --
2. Reflection functors and change of orientation [172] --
3. Weyl group and reflection functors [172] --
4. Coxeter functors [173] --
5. Further properties of Coxeter functors [174] --
6. Affine root systems [177] --
7 Preprojective and preiniective representations [179] --
8. Regular representations [182] --
9. Indecomposable representations of affine quivers [189] --
Chapter 9. Applications of quivers [193] --
1. From abelian categories to algebras [193] --
2. From categories to quivers [195] --
3. Finitely represented, tame and wild algebras [199] --
4. Frobenius algebras [200] --
5. Application to group algebras [202] --
6. On certain categories of -modules [205] --
Bibliography [219] --
Index [221] --
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