On the density of fiber sum factors.
On the derived category of a finite-dimensional algebra.
On the existence of almost split sequences in subcategories
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 Freyd categories of an additive category.
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 lattice of cotilting modules.
On the number of terms in the middle of almost split sequences over cycle-finite artin algebras
We prove that the number of terms in the middle of an almost split sequence in the module category of a cycle-finite artin algebra is bounded by 5.
On the numbers of discrete indecomposable modules over tame algebras
On the problem of axiomatization of tame representation type
Associative algebras of fixed dimension over algebraically closed fields of fixed characteristic are considered. It is proved that the class of algebras of tame representation type is axiomatizable. Moreover, finite axiomatizability of this class is equivalent to the conjecture that the algebras of tame representation type form a Zariski-open subset in the variety of algebras.
On the Represantation Theory of Artinian Rings and Artins Problems on Division Ring Extensions
On the representation type of one point extensions of tame concealed algebras.
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 representation type of triangular matrix algebras over special algebras
On the structure of Calabi-Yau categories with a cluster tilting subcategory.
On the structure of indecomposable modules over Artin algebras
On the structure of locally finite pure semisimple Grothendieck categories
On the structure of triangulated categories with finitely many indecomposables
We study the problem of classifying triangulated categories with finite-dimensional morphism spaces and finitely many indecomposables over an algebraically closed field . We obtain a new proof of the following result due to Xiao and Zhu: the Auslander-Reiten quiver of such a category is of the form where is a disjoint union of simply-laced Dynkin diagrams and a weakly admissible group of automorphisms of . Then we prove that for ‘most’ groups , the category is standard,i.e.-linearly...
On the tameness of trivial extension algebras
For a finite dimensional algebra A over an algebraically closed field, let T(A) denote the trivial extension of A by its minimal injective cogenerator bimodule. We prove that, if is a tilting module and , then T(A) is tame if and only if T(B) is tame.