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On cyclic vertices in valued translation quivers

Piotr Malicki — 2006

Colloquium Mathematicae

Let x and y be two vertices lying on an oriented cycle in a connected valued translation quiver (Γ,τ,δ). We prove that, under certain conditions, x and y belong to the same cyclic component of (Γ,τ,δ) if and only if there is an oriented cycle in (Γ,τ,δ) passing through x and y.

Hochschild cohomology of generalized multicoil algebras

Piotr MalickiAndrzej Skowroński — 2014

Colloquium Mathematicae

We determine the Hochschild cohomology of all finite-dimensional generalized multicoil algebras over an algebraically closed field, which are the algebras for which the Auslander-Reiten quiver admits a separating family of almost cyclic coherent components. In particular, the analytically rigid generalized multicoil algebras are described.

Indecomposable modules in coils

Piotr MalickiAndrzej SkowrońskiBertha Tomé — 2002

Colloquium Mathematicae

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.

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