On Generalized Uniserial Rings and Decompositions that Complement Direct Summands.
On hereditary artinian rings and the pure semisimplicity conjecture: rigid tilting modules and a weak conjecture
A weak form of the pure semisimplicity conjecture is introduced and characterized through properties of matrices over division rings. The step from this weak conjecture to the full pure semisimplicity conjecture would be covered by proving that there do not exist counterexamples to the conjecture in a particular class of rings, which is also studied.
On hereditary rings and the pure semisimplicity conjecture II: Sporadic potential counterexamples
It was shown in [Colloq. Math. 135 (2014), 227-262] that the pure semisimplicity conjecture (briefly, pssC) can be split into two parts: first, a weak pssC that can be seen as a purely linear algebra condition, related to an embedding of division rings and properties of matrices over those rings; the second part is the assertion that the class of left pure semisimple sporadic rings (ibid.) is empty. In the present article, we characterize the class of left pure semisimple sporadic rings having finitely...
On Hom-spaces of tame algebras
Let Λ be a finite dimensional algebra over an algebraically closed field k and Λ has tame representation type. In this paper, the structure of Hom-spaces of all pairs of indecomposable Λ-modules having dimension smaller than or equal to a fixed natural number is described, and their dimensions are calculated in terms of a finite number of finitely generated Λ-modules and generic Λ-modules. In particular, such spaces are essentially controlled by those of the corresponding generic modules.
On indecomposable projective representations of finite groups over fields of characteristic p > 0
Let G be a finite group, F a field of characteristic p with p||G|, and the twisted group algebra of the group G and the field F with a 2-cocycle λ ∈ Z²(G,F*). We give necessary and sufficient conditions for to be of finite representation type. We also introduce the concept of projective F-representation type for the group G (finite, infinite, mixed) and we exhibit finite groups of each type.
On indecomposable representations of quivers with zero-relations
On induced modules over strongly group-graded algebras.
On intecomposable Lattices over Twisted group rings
On large selforthogonal modules
We construct non faithful direct summands of tilting (resp. cotilting) modules large enough to inherit a functorial tilting (resp. cotilting) behaviour.
On locally bounded categories stably equivalent to the repetitive algebras of tubular algebras
On minimal non-tilted algebras
A minimal non-tilted triangular algebra such that any proper semiconvex subcategory is tilted is called a tilt-semicritical algebra. We study the tilt-semicritical algebras which are quasitilted or one-point extensions of tilted algebras of tame hereditary type. We establish inductive procedures to decide whether or not a given strongly simply connected algebra is tilted.
On module categories with nilpotent infinite radical
On modules with Le-decomposition.
On Morphisms between Indecomposable Projective Modules over Special Biserial Algebras
We investigate the categorical behaviour of morphisms between indecomposable projective modules over a special biserial algebra A over an algebraically closed field, which are associated to arrows of the Gabriel quiver of A.
On Multiplicative Bases in Quasi Frobenius Algebras.
On nonexistence of oriented cycles in Auslander-Reiten quivers
On nonstandard tame selfinjective algebras having only periodic modules
We investigate degenerations and derived equivalences of tame selfinjective algebras having no simply connected Galois coverings but the stable Auslander-Reiten quiver consisting only of tubes, discovered recently in [4].
On path coalgebras of quivers with relations
The notion of the path coalgebra of a quiver with relations introduced in [11] and [12] is studied. In particular, developing this topic in the context of the weak* topology, we give a criterion that allows us to verify whether or not a relation subcoalgebra of a path coalgebra is the path coalgebra of a quiver with relations.
On perpendicular categories of stones over quiver algebras.
On pure semi-simple Grothendieck categories I