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Tables of Contents for Representation Theory of Group Graded Algebras
Chapter/Section Title
Page #
Page Count
Preface
vii
Modules Over Graded Rings
1
50
Categories of modules graded by G-sets
1
8
Construction of functors
2
5
Transitive G-sets. The grade-forgetting functor
7
2
Groups of graded homomorphisms. The coinduction functor
9
4
The coinduction functor
12
1
The induction functor and strongly graded rings
13
6
Crossed products
15
2
The smash product and duality
17
2
Relative projectivity and the Green Correspondence
19
12
Induction, coinduction and restriction
19
3
Relative projectivity
22
6
Vertices, sources, and the Green Correspondence
28
3
Graded simple modules and the graded Jacobson radical
31
6
Simple objects in R-Gr and the graded Jacobson radical
35
2
Graded bimodules
37
7
The Brauer correspondence for bimodules and blocks
44
7
Clifford Theory
51
38
Static modules and induction
51
4
The endomorphism ring of a graded module
55
3
The Clifford correspondence
58
13
The general correspondence
59
4
Clifford theory of simple and indecomposable modules
63
5
Compounded Clifford correspondences
68
1
Clifford theory for arbitrary subgroups
69
2
Applications of the Clifford correspondence
71
13
Clifford theory for projective modules
72
7
Algebras graded by p-solvable groups
79
4
The Loewy length of induced modules
83
1
Clifford theory of bimodules and blocks
84
5
Bimodules lying over an (R1, S1)-bimodule
84
3
The Clifford correspondence
87
2
Clifford Extensions
89
26
Extending simple and indecomposable R1-modules
89
8
Extendability criteria
97
10
Crossed products and central simple algebras
98
2
The obstruction to the extendibility of an R1-module
100
2
The determinantal representation
102
1
Comparing obstructions
103
2
Reduction to PF -elementary subgroups
105
2
G/H-invariant extensions
107
8
Auslander--Reiten Theory
115
44
Functor categories and relative projectivity
115
10
Indecomposable modules and simple functors
125
8
Almost split sequences and Clifford theory
133
11
The decomposition of IndG1SV
133
3
Inducing irreducible maps
136
2
Vertices of simple functors
138
5
Extendability of simple functors
143
1
Functor categories and equivalences
144
8
Clifford correspondence for functor categories
144
3
Middle terms of short exact sequences
147
5
Module correspondences in Auslander-Reiten quivers
152
7
Green correspondence
152
4
Auslander-Reiten quivers and Clifford theory
156
3
Equivalences Induced by Graded Bimodules
159
44
Morita equivalences
159
21
Symmetric algebras
164
2
Invariants of graded Morita equivalences
166
4
Equivalences for wreath products
170
2
Local structure of graded Morita equivalences
172
4
Picard groups
176
4
Derived equivalences
180
8
Symmetric algebras
183
2
Equivalences for wreath products
185
3
Stable Morita equivalences
188
6
The Heller operator
191
2
Symmetric algebras
193
1
Homology of strongly graded algebras
194
9
The spectral sequences
194
3
Invariance under Morita and derived equivalence
197
3
Cyclic homology of graded algebras
200
3
Bibliography
203
6
Index
209