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