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Iterated coil enlargements of algebras

100%

Tomé B.

Fundamenta Mathematicae

1994-1995

tom 146

nr 3

251-266

Let Λ be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Λ be the category of finitely generated right Λ-modules. We say that Λ has acceptable projectives if the indecomposable projective Λ-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Λ the following conditions are equivalent: (a) Λ is tame, (b) the Tits form $q_Λ$ of Λ is weakly non-negative, (c)~Λ is an iterated coil enlargement

Strongly simply connected coil algebras

51%

Coelho F. , Martins M. , Tomé B.

Colloquium Mathematicum

2004

tom 99

nr 1

91-110

We study the simple connectedness and strong simple connectedness of the following classes of algebras: (tame) coil enlargements of tame concealed algebras and n-iterated coil enlargement algebras.

Indecomposable modules in coils

51%

Malicki P. , Skowroński A. , Tomé B.

Colloquium Mathematicum

2002

tom 93

nr 1

67-130

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.