Comparison of Auslander-Reiten theory and Gabriel-Roiter measure approach to the module categories of tame hereditary algebras
نویسنده
چکیده
Let Λ be a tame hereditary algebra over an algebraically closed field, i.e. Λ = kQ with Q a quiver of type Ãn, D̃n, Ẽ6, Ẽ7, or Ẽ8. Two different kinds of partitions of the module category can be obtained by using Auslander-Reiten theory, and on the other hand, Gabriel-Roiter measure approach. We compare these two kinds of partitions and see how the modules are rearranged according to Gabriel-Roiter measure. We also show that the Gabriel-Roiter submodules can be used to build orthogonal exceptional pairs for indecomposable preprojective Λ-modules when Λ is of type Ãn,n≥2 and D̃n.
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