## Coxeter spectral classification of almost TP-critical one-peak posets using symbolic and numeric computations

Published in Linear Algebra and Its Applications

Published in Linear Algebra and Its Applications

Published in Advances in Mathematics

We study the singularity category of the triangle singularity f=xa+yb+zc, or S=k[x,y,z]/(f), attached to the weighted projective line X, given by the weight triple (a,b,c), by investigating the stable category vect¯-X of vector bundles on X, obtained from the category of vector bundles by factoring out all the line bundles.We show that vect¯-X is f...

Published in Advances in Mathematics

Given an n-tuple of positive real numbers α we consider the hyperpolygon space X(α), the hyperkähler quotient analogue to the Kähler moduli space of polygons in R3. We prove the existence of an isomorphism between hyperpolygon spaces and moduli spaces of stable, rank-2, holomorphically trivial parabolic Higgs bundles over CP1 with fixed determinant...

Published in Journal of Algebra

We present a general solution of the isomorphism and multiplicity problems, restricted to the class of all modules lying in homogeneous tubes, for tame algebras (Theorem 2.4). We introduce a notion of the characteristic polynomial of a module, which plays an analogous role as in the classical situation. This notion uses a Smith form Δ(HB(M)) of cer...

Published in Journal of Algebra

Published in Advances in Mathematics

From the viewpoint of higher dimensional Auslander–Reiten theory, we introduce a new class of finite dimensional algebras of global dimension n, which we call n-representation infinite. They are a certain analog of representation infinite hereditary algebras, and we study three important classes of modules: n-preprojective, n-preinjective and n-reg...

Published in Journal of Algebra

For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.

Published in Journal of Algebra

A finite EI category is a small category with finitely many morphisms such that every endomorphism is an isomorphism. They include finite groups, finite posets and free categories of finite quivers as special cases. In this paper we consider category algebras of finite EI categories with two or three objects, describe some criteria for finite repre...

Published in Forum Mathematicum

We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic branching systems, to which irreducible representations of the Leavitt path algebra are associated. For a certain quiv...