On minimal disjoint degenerations of modules over tame path algebras

On minimal disjoint degenerations of modules over tame path algebras

For representations of tame quivers the degenerations are controlled by the dimensions of various homomorphism spaces. Furthermore, there is no proper degeneration to an indecomposable. Therefore, up to common direct summands, any minimal degeneration from M to N is induced by a short exact sequence 0 → U → M → V → 0 with indecomposable ends that add up to N . We study these ’building blocs’ of...

Degenerations for Modules over Representation-finite Biserial Algebras

On minimal disjoint degenerations for preprojective representations of quivers

We derive a root test for degenerations as described in the title. In the case of Dynkin quivers this leads to a conceptual proof of the fact that the codimension of a minimal disjoint degeneration is always one. For Euclidean quivers, it enables us to show a periodic behaviour. This reduces the classification of all these degenerations to a finite problem that we have solved with the aid of a ...

On the Finsler modules over H-algebras

In this paper, applying the concept of generalized A-valued norm on a right $H^*$-module and also the notion of ϕ-homomorphism of Finsler modules over $C^*$-algebras we first improve the definition of the Finsler module over $H^*$-algebra and then define ϕ-morphism of Finsler modules over $H^*$-algebras. Finally we present some results concerning these new ones.

Category equivalences involving graded modules over path algebras of quivers

Let Q be a finite quiver with vertex set I and arrow set Q1, k a field, and k Q its path algebra with its standard grading. This paper proves some category equivalences involving the quotient category QGr(k Q) := Gr(k Q)/Fdim(k Q) of graded k Q-modules modulo those that are the sum of their finite dimensional submodules, namely QGr(k Q) ≡ ModS(Q) ≡ GrL(Q) ≡ ModL(Q◦)0 ≡ QGr(k Q (n)). Here S(Q) =...