Bobiński, Grzegorz Skowroński, Andrzej
Published in
Open Mathematics

In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit ...

Białkowski, J. Skowroński, A.
Published in
Archiv der Mathematik

We classify (up to Morita equivalence) all tame weakly symmetric finite dimensional algebras over an algebraically closed field having simply connected Galois coverings, nonsingular Cartan matrices and the stable Auslander-Reiten quivers consisting only of tubes. In particular, we prove that these algebras have at most four simple modules.

Li, Li-Bin
Published in
Archiv der Mathematik

In this article, we discuss the infinite dimensional indecomposable Harish-Chandra representations over ${\cal U}_q(sl(2))$. As an application, we answer a question of Ringel on the annihilator ideals of simple modules.

Erdmann, Karin Holm, Thorsten Iyama, Osamu Schröer, Jan
Published in
Advances in Mathematics

Given a representation-finite algebra B and a subalgebra A of B such that the Jacobson radicals of A and B coincide, we prove that the representation dimension of A is at most three. By a result of Igusa and Todorov, this implies that the finitistic dimension of A is finite.

Zhu, Bin Hu, Zong Yi
Published in
Acta Mathematica Sinica

We single out a class of translation quivers and prove combinatorially that the translation quivers in this class are coils. These coils form a class of special coils. They are easier to visualize, but still show all the strange behaviour of general coils, and contain quasi-stable tubes as special examples.

Zhang, Pu
Published in
Advances in Mathematics

By introducing a twisted Hopf algebra we unify several important objects of study. Skew derivations of such an algebra are defined and the corresponding skew differential operator algebras are studied. This generalizes results in the Weyl algebra. Applying this investigation to the twisted Ringel–Hall algebra we get, in particular, a natural realiz...