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...

Hiroe, Kazuki

In this note, we will explain symmetries of isomonodromic deformations as Weyl groups of some quivers and give classifications of isomondromic deformations of linear ordinary differential equations with at most unramified irregular singularities and 2 or 4 accessory parameters.

Coelho Simões, Raquel
Published in
Forum Mathematicum

In this article, we give a definition and a classification of ‘higher’ simple-minded systems in triangulated categories generated by spherical objects with negative Calabi–Yau dimension. We also study mutations of this class of objects and that of ‘higher’ Hom-configurations and Riedtmann configurations. This gives an explicit analogue of the ‘nice...

Sakurai, Taro

The Loewy structure of a module can be viewed as a q-analog of its composition factors. From this point of view we define q-composition multiplicity; q-composition length, and the q-Cartan matrix. By way of example, group algebras of finite p-groups and path algebras of finite acyclic quivers are investigated. Some known results for these algebras ...

Sakurai, Taro

The Loewy structure of a module can be viewed as a q-analog of its composition factors. From this point of view we define q-composition multiplicity; q-composition length, and the q-Cartan matrix. By way of example, group algebras of finite p-groups and path algebras of finite acyclic quivers are investigated. Some known results for these algebras ...

Sakurai, Taro

The Loewy structure of a module can be viewed as a q-analog of its composition factors. From this point of view we define q-composition multiplicity; q-composition length, and the q-Cartan matrix. By way of example, group algebras of finite p-groups and path algebras of finite acyclic quivers are investigated. Some known results for these algebras ...

Holm, Thorsten Jørgensen, Peter
Published in
Forum Mathematicum

This paper shows a new phenomenon in higher cluster tilting theory. For each positive integer d, we exhibit a triangulated category 𝖢 with the following properties. On the one hand, the d-cluster tilting subcategories of 𝖢 have very simple mutation behaviour: Each indecomposable object has exactly d mutations. On the other hand, the weakly d-cluste...

Hille, Lutz Müller, Jürgen
Published in
Linear Algebra and Its Applications

We derive a formula for the Coxeter polynomial of the s-fold tensor product ⨂i=1sF[A→ni−1] of path algebras of linearly oriented quivers of Dynkin type Ani−1, in terms of the weights n1,…,ns≥2, and show that conversely the weights can be recovered from the Coxeter polynomial of the tensor product. Our results have relevance in singularity theory, i...

Holdaway, Cody Sisodia, Gautam
Published in
Journal of Algebra

Let k be a field, Q a finite directed graph, and kQ its path algebra. Make kQ an N-graded algebra by assigning each arrow a positive degree. Let I be an ideal in kQ generated by a finite number of paths and write A=kQ/I. Let QGrA denote the quotient of the category of graded right A-modules modulo the Serre subcategory consisting of those graded mo...

Hille, Lutz Müller, Jürgen
Published in
Linear Algebra and Its Applications