On perpendicular categories of stones over quiver algebras.
On quasitilted algebras which are one-point extensions of hereditary algebras
Quasitilted algebras have been introduced as a proper generalization of tilted algebras. In an earlier article we determined necessary conditions for one-point extensions of decomposable finite-dimensional hereditary algebras to be quasitilted and not tilted. In this article we study algebras satisfying these necessary conditions in order to investigate to what extent the conditions are sufficient.
On restrictions of indecomposables of tame algebras
We continue the study of ditalgebras, an acronym for "differential tensor algebras", and of their categories of modules. We examine extension/restriction interactions between module categories over a ditalgebra and a proper subditalgebra. As an application, we prove a result on representations of finite-dimensional tame algebras Λ over an algebraically closed field, which gives information on the extension/restriction interaction between module categories of some special algebras Λ₀, called convex...
On self-injective algebras of finite representation type
We describe the structure of finite-dimensional self-injective algebras of finite representation type over a field whose stable Auslander-Reiten quiver has a sectional module not lying on a short chain.
On semi-invariants of tilted algebras of type Aₙ
We prove that for algebras obtained by tilts from the path algebras of equioriented Dynkin diagrams of type Aₙ, the rings of semi-invariants are polynomial.
On some formulas in the Hall algebra of the Kronecker algebra.
On the deformation theory of finite dimensional algebras.
On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth
Assume that k is a field of characteristic different from 2. We show that if Γ is a strongly simply connected k-algebra of non-polynomial growth, then there exists a special family of pointed Γ-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that Γ admits a super-decomposable pure-injective module if k is a countable field.
On the genus of the graph of tilting modules.
On the K-theory of tubular algebras
Let Λ be a tubular algebra over an arbitrary base field. We study the Grothendieck group , endowed with the Euler form, and its automorphism group on a purely K-theoretical level as in [7]. Our results serve as tools for classifying the separating tubular families of tubular algebras as in the example [5] and for determining the automorphism group of the derived category of Λ.
On the representation type of tensor product algebras
The representation type of tensor product algebras of finite-dimensional algebras is considered. The characterization of algebras A, B such that A ⊗ B is of tame representation type is given in terms of the Gabriel quivers of the algebras A, B.
On the trivial extensions of tubular algebras
The aim of this note is to give an affirmative answer to a problem raised in [9] by J. Nehring and A. Skowroński, concerning the number of nonstable ℙ₁(K)-families of quasi-tubes in the Auslander-Reiten quivers of the trivial extensions of tubular algebras over algebraically closed fields K.
On the zero set of semi-invariants for quivers
On transitive systems of subspaces in a Hilbert space.
On triangulated orbit categories.
On two tame algebras with super-decomposable pure-injective modules
Let k be a field of characteristic different from 2. We consider two important tame non-polynomial growth algebras: the incidence k-algebra of the garland 𝒢₃ of length 3 and the incidence k-algebra of the enlargement of the Nazarova-Zavadskij poset 𝒩 𝓩 by a greatest element. We show that if Λ is one of these algebras, then there exists a special family of pointed Λ-modules, called an independent pair of dense chains of pointed modules. Hence, by a result of Ziegler, Λ admits a super-decomposable...
On wings of the Auslander-Reiten quivers of selfinjective algebras
We give necessary and sufficient conditions for a wing of an Auslander-Reiten quiver of a selfinjective algebra to be the wing of the radical of an indecomposable projective module. Moreover, a characterization of indecomposable Nakayama algebras of Loewy length ≥ 3 is obtained.
One point extensions of trees and quadratic forms
One-directed indecomposable pure injective modules over string algebras
We classify one-directed indecomposable pure injective modules over finite-dimensional string algebras.
Partial flag varieties and preprojective algebras
Let be a preprojective algebra of type , and let be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories for an injective -module, and we introduce a mutation operation between complete rigid modules in . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to .