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...

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.

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.

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 ...

Bobiński, Grzegorz Skowroński, Andrzej
Published in
Open Mathematics

In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodi...

Kleiner, Mark Tyler, Helene R.
Published in
Advances in Mathematics

This paper concerns indecomposable preprojective modules over the path algebra of a finite connected quiver without oriented cycles. For each such module, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection func...

Lin, Yanan Peng, Liangang
Published in
Advances in Mathematics

This article is to study relations between tubular algebras of Ringel and elliptic Lie algebras in the sense of Saito–Yoshii. Using the explicit structure of the derived categories of tubular algebras given by Happel–Ringel, we prove that the elliptic Lie algebra of type D 4 ( 1 , 1 ) , E 6 ( 1 , 1 ) , E 7 ( 1 , 1 ) or E 8 ( 1 , 1 ) is isomorphic t...

Enomoto, Masatoshi 榎本, 雅俊 Watatani, Yasuo 綿谷, 安男

The relative position of one subfactor of a factor has been proved quite rich since the work of Jones. We shall show that the theory of relative position of several subspaces of a separable infinite-dimensional Hilbert space is also rich. In finite-dimensonal case, Gelfand and Ponomarev gave a complete classification of indecomposable systems of fo...