Chapoton, Frédéric Rognerud, Baptiste
Published in
Algebras and Representation Theory

In this note, we investigate the representation type of the cambrian lattices and some other related lattices. The result is expressed as a very simple trichotomy. When the rank of the underlined Coxeter group is at most 2, the lattices are of finite representation type. When the Coxeter group is a reducible group of type A13\documentclass[12pt]{mi...

Garver, Alexander McConville, Thomas
Published in
Algebras and Representation Theory

The exchange graph of a 2-acyclic quiver is the graph of mutation-equivalent quivers whose edges correspond to mutations. When the quiver admits a nondegenerate Jacobi-finite potential, the exchange graph admits a natural acyclic orientation called the oriented exchange graph, as shown by Brüstle and Yang. The oriented exchange graph is isomorphic ...

Kosakowska, Justyna Schmidmeier, Markus
Published in
Mathematische Zeitschrift

Given partitions α,β,γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ,\beta ,\gamma $$\end{document}, the short exact sequences 0⟶Nα⟶Nβ⟶Nγ⟶0\documentclass[12pt]...

Erdmann, Karin Skowroński, Andrzej
Published in
Algebras and Representation Theory

We introduce and study the higher tetrahedral algebras, an exotic family of finite-dimensional tame symmetric algebras over an algebraically closed field. The Gabriel quiver of such an algebra is the triangulation quiver associated to the coherent orientation of the tetrahedron. Surprisingly, these algebras occurred in the classification of all alg...

Dowbor, Piotr Meltzer, Hagen
Published in
Algebras and Representation Theory

Formulas for the dimension vectors of all objects M in the category S(6~)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {S}(\tilde {6})$\end{document} of nilpo...

Adachi, Takahide Aihara, Takuma Chan, Aaron
Published in
Mathematische Zeitschrift

Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an application, we determine precisely the class of Brauer graph algebras which are tilting-discrete.

Koç, Ayten Özaydın, Murad
Published in
Forum Mathematicum

When Γ is a row-finite digraph, we classify all finite-dimensional modules of the Leavitt path algebra L ( Γ ) {L(\Gamma)} via an explicit Morita equivalence given by an effective combinatorial (reduction) algorithm on the digraph Γ. The category of (unital) L ( Γ ) {L(\Gamma)} -modules is equivalent to a full subcategory of quiver representati...

Assem, Ibrahim Schiffler, Ralf Serhiyenko, Khrystyna
Published in
Archiv der Mathematik

We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number of (isoclasses of) these modules.

Craw, Alastair Green, James
Published in
European Journal of Mathematics

We prove that every toric quiver flag variety Y is isomorphic to a fine moduli space of cyclic modules over the algebra End(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docum...

Craw, Alastair Ito, Yukari Karmazyn, Joseph
Published in
Mathematische Zeitschrift

Given a scheme Y equipped with a collection of globally generated vector bundles E1,…,En\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_1, \ldots , E_n$$\end{document...