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...
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...
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 ...
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...
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...
Published in Linear Algebra and Its Applications
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...
Published in Journal of Algebra
Published in Advances in Mathematics
Published in Linear Algebra and Its Applications
