Indecomposable modules in coils
Tom 93 / 2002
Colloquium Mathematicum 93 (2002), 67-130 MSC: 16G20, 16G60, 16G70. DOI: 10.4064/cm93-1-7
We describe the structure of all indecomposable modules in standard coils of the Auslander–Reiten quivers of finite-dimensional algebras over an algebraically closed field. We prove that the supports of such modules are obtained from algebras with sincere standard stable tubes by adding braids of two linear quivers. As an application we obtain a complete classification of non-directing indecomposable modules over all strongly simply connected algebras of polynomial growth.