Quasi-hereditary algebras and the geometry of representations of algebras

Introduction......Page 7
Additive categories......Page 12
Module categories......Page 13
Auslander-Reiten theory......Page 15
Representations of quivers......Page 17
Representations varieties and their group actions......Page 18
Fibre bundles......Page 20
Flag varieties......Page 21
Quasi-hereditary algebras......Page 22
Strongly quasi-hereditary algebras......Page 24
Tensor algebras......Page 26
Overview......Page 28
Submodule categories......Page 29
Representations of the Auslander algebra......Page 30
The Auslander algebra of self-injective algebras......Page 34
Recollement......Page 35
Induced equivalences......Page 36
Interplay with triangulated structure......Page 39
Auslander algebras of Nakayama algebras......Page 40
Auslander algebras of Nakayama algebras......Page 41
Other representation-finite algebras......Page 43
Overview......Page 45
Monomorphism categories......Page 46
Quasi-hereditary structure......Page 47
AR-translates in monomorphism categories......Page 49
Quiver flag varieties......Page 52
Adding relations......Page 55
Long exact sequence......Page 57
Ext-directed decompositions......Page 58
Overview......Page 61
Quiver-graded Richardson orbits......Page 62
The nilpotent quiver algebra......Page 66
Tensor structures......Page 67
Monomorphism categories and the category N......Page 70
Ns(Q) as an endomorphism ring......Page 73
Quasi-hereditary structure of the nilpotent quiver algebra......Page 76
The Ringel-dual......Page 81
Rigid -filtered modules correspond to Richardson orbits......Page 85
Examples......Page 86
Algorithm for Q = A2......Page 88
Bibliography......Page 91
Index......Page 96