Coxeter spectral classification of almost TP-critical one-peak posets using symbolic and numeric computations
Published in Linear Algebra and Its Applications
Triangle singularities, ADE-chains, and weighted projective lines
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...
Hyperpolygon spaces and moduli spaces of parabolic Higgs bundles
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...
On the normal forms of modules with respect to parametrizing bimodules
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...
On the normal forms of modules with respect to parametrizing bimodules
Published in Journal of Algebra
n-representation infinite algebras
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...
On the representation types of category algebras of finite EI categories
Published in Journal of Algebra
Systems of subspaces of a unitary space
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.
On the representation types of category algebras of finite EI categories
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...
Irreducible representations of Leavitt path algebras
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...
