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König S., Zimmermann A. — Derived Equivalences For Group Rings
König S., Zimmermann A. — Derived Equivalences For Group Rings

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Название: Derived Equivalences For Group Rings

Авторы: König S., Zimmermann A.

Аннотация:

A self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broué's conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 246

Добавлена в каталог: 04.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathbf{D}\mathfrak{C}$      16
$\mathbf{K}(\mathfrak{C})$      7
$\mathcal{C}$-local module      195
$\mathcal{O}$-stable category      201
Alperin conjecture      52 188
Alperin MacKay conjecture      52
Basic ring      74
Beilinson equivalence      168
Bijection with signs      135 186
Biserial      65
Block      54 185
Block algebra      185
Bousfield localization      193
Brauer construction      190
Brauer correspondent      64 210
Brauer tree      65 213
Brauer tree algebra      65
Brauer tree algebras; derived equivalent      91 199
Brauer, R.      64
Brenner — Butler theorem      35
Broue conjecture      52 132 135 188
Broue conjecture on perfect isometries      133 135 188
Broue conjecture, weak form      133 135
Broue conjecture; extension to splendid equivalences      193
C      6
Cartan Brauer triangle      61
Cartan mapping      58
Cartan matrix      58 104
cde-triangle      61
Chain complex      178
Cochain complex      178
Cohomological functor      13
Cohomology of a complex      7
Compact functor      160
Compatible family of derived equivalences      189
COMPLEX      6
Complex, bounded      6
Complexity of a module      195
Connected graph      65
Control of fusion      192
Cyclic defect      66 199
Cyclic homology      169
Dade, E.      66
Decomposition mapping      58
Decomposition matrix      59
Decomposition numbers      59
Decomposition numbers of cyclic blocs      212
Defect      55
Defect group      55
Deligne — Lusztig varietiy      190
Derived category      16 164
Derived category of a hereditary algebra      19
Derived equivalence of standard type      112 160
Derived functor      20
Derived functor, left      159
Derived functor, right      159
Devissage      158
DG-algebra      162
Differential      6
Differential graded algebra      162
Differential graded module      163
Dihedral defect group      101
Distinguished triangle      10 163
Double complex      21
Dual module      180
Duality      180
e-subpair      210
Edges of a graph      65
Epaisse subcategory      194
Equivalence induced by a tilting complex      108
Euler characteristic      117
Exceptional character      66 211
Exceptional vertex      65 211
Exceptional vertex, multiplicity of exceptional vertex      65
Gabriel quiver      103
Gabriel's theorem      33
Gabriel, P.      103
Generator of a triangulated category      161
Generic Green order      70
Gorenstein order      81
Graph      65
Graph orders      104
Green correspondence      61
Green order      69 72
Green orders; derived equivalent      91
Green, J.A.      61 69
Grothendieck group      58 117
Higman, D.      53
Hochschild cohomology      122
Hochschild complex      170
Hochschild homology      171
Homotopic to zero      6 7
Homotopically injective complex      156
Homotopically injective DG-module      164
Homotopically projective complex      156
Homotopically projective DG-module      164
Homotopy      6
Homotopy category      7 163 164
Infinite devissage      158
Isometry      132
Isotypic order      73
Isotypy      189
K-theoretic equivalence      169
K-theory, invariant under derived equivalence      116
l-adic cohomology      190
Leaf      69
Localization (at a multiplicative system)      15
Localization of categories      158 164
Mapping cone      8 164
Milnor's triangle      156
Mittag-Leffler condition      23
Multiplicative system      15
Multiplicity of a vertex      65
Nakayama algebra      65
No loops conjecture      170
Null system      16
Null-homotopic      163
Octahedral axiom      11
p-permutation module      189
Packard complex      203
Packard equivalence      200 203
Packard's fundamental theorem      36
Partial tilting complex      36
Perfect character      130
Perfect complex      160
Perfect isometry      132 187
Permutation module      189
Principal block      185
Projective free part of a module      194
Projective resolution of complexes      113 125
Projective system      22
Qis      14
Quasi-isomorphism      14 164
quiver      103
R-projective      53 123
R-stable category      123
Relatively projective      53 123
Repetative algebra      168
Representation type      103
Right derived functor      20
serial      65
Shift functor      6
Source      53
Splendid equivalence      191 199 204
Splendid tilting complex      191
Split endomorphism tilting complex      184
Stable (module) category      13
Stable categories      168
Stable category      201
Stable equivalence      200
Stable equivalence of Morita type      123
Stable isomorphism      194
Stable module category      193
Standard derived equivalence      112 160
Standard triangle      163
Standard type      112 160
Subpair      210
Suspension functor      157 163
Symmetric algebra      64 179
Syzygy      64
Tame representation type      103
Tilting complex      36
Tilting complexes and group extensions      205
Tilting module      34
Toda condition      166
Total complex      22
Translation functor      157
TREE      65
triangle      10
Triangulated category      11
Trivial source module      189
Two sided tilting complex      105 166 183
Unbounded derived category      158
Uniserial      65
Varieties for infinitely generated modules      196
Variety of modules      194
Vertex of a graph      65
Vertex of a module      53
Walk around the Brauer tree      67 213
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