Survey on the reprensentation type of group algebras
Tubular mutations
Auslander-Reiten components for concealed-canonical algebras
Derived tubular algebras and APR-tilts
The global basie dimension of artin rings
CONTENTS1. Introduction.............52. Basic dimension of artin rings................73. Cobasic dimension of artin rings............84. Basic dimension of algebras stably equivalent to an hereditary artin algebra............125. Hereditary artin algebras of global basic and cobasic dimension 1....................176. Global basic and cobasic dimensions of radical squared zero algebras............34References...............43
Correction to: "Group Algebras of Finite Representation Type". Math. Z. 182, 129 - 148 (1983).
Group Algebras of Finite Representation Type.
Indecomposable representations for extended Dynkin quivers of type 𝔼̃₈
We discuss the problem of classification of indecomposable representations for extended Dynkin quivers of type 𝔼̃₈, with a fixed orientation. We describe a method for an explicit determination of all indecomposable preprojective and preinjective representations for those quivers over an arbitrary field and for all indecomposable representations in case the field is algebraically closed. This method uses tilting theory and results about indecomposable modules for a canonical algebra of type (5,3,2)...
Matrix factorizations for domestic triangle singularities
Working over an algebraically closed field k of any characteristic, we determine the matrix factorizations for the-suitably graded-triangle singularities of domestic type, that is, we assume that (a,b,c) are integers at least two satisfying 1/a + 1/b + 1/c > 1. Using work by Kussin-Lenzing-Meltzer, this is achieved by determining projective covers in the Frobenius category of vector bundles on the weighted projective line of weight type (a,b,c). Equivalently, in a representation-theoretic context,...
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