A Class of Infinite-Rank Modules over Tame Hereditary 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...

On Ringel-hall Algebras of Tame Hereditary Algebras

Cluster algebras of infinite rank

Holm and Jørgensen have shown the existence of a cluster structure on a certain category D that shares many properties with finite type A cluster categories and that can be fruitfully considered as an infinite analogue of these. In this work we determine fully the combinatorics of this cluster structure and show that these are the cluster combinatorics of cluster algebras of infinite rank. That...

- Algebras of Infinite Real Rank

We introduce the notion of weakly (strongly) infinite real rank for unital C∗-algebras. It is shown that a compact space X is weakly (strongly) infine-dimensional if and only if C(X) has weakly (strongly) infinite real rank. Some other properties of this concept are also investigated. In particular, we show that the group C∗-algebra C∗ (F∞) of the free group on countable number of generators ha...

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.