Finite dimensional algebras and highest weight categories.
Finite Dimensional Hereditary Algebras of Wild Representation Type.
Finite groups of OTP projective representation type
Let K be a field of characteristic p > 0, K* the multiplicative group of K and a finite group, where is a p-group and B is a p’-group. Denote by a twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for G to be of OTP projective K-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,K*) such that every indecomposable -module is isomorphic to the outer tensor product V W of an indecomposable -module V and a simple...
Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic
Let S be a commutative complete discrete valuation domain of positive characteristic p, S* the unit group of S, Ω a subgroup of S* and a finite group, where is a p-group and B is a p’-group. Denote by the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). For Ω satisfying a specific condition, we give necessary and sufficient conditions for G to be of OTP projective (S,Ω)-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,Ω) such that every indecomposable...
Finite mutation classes of coloured quivers
We show that the mutation class of a coloured quiver arising from an m-cluster tilting object associated with a finite-dimensional hereditary algebra H, is finite if and only if H is of finite or tame representation type, or it has at most two simples. This generalizes a result known for cluster categories.
Finite-dimensional twisted group algebras of semi-wild representation type
Let G be a finite group, K a field of characteristic p > 0, and the twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for to be of semi-wild representation type in the sense of Drozd. We also introduce the concept of projective K-representation type for a finite group (tame, semi-wild, purely semi-wild) and we exhibit finite groups of each type.
Finiteness of the strong global dimension of radical square zero algebras
The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density...
Flat covers of representations of the quiver .
F-semiperfeke und perfekte Moduln in ... [M].
Full embeddings of almost split sequences over split-by-nilpotent extensions
Let R be a split extension of an artin algebra A by a nilpotent bimodule , and let M be an indecomposable non-projective A-module. We show that the almost split sequences ending with M in mod A and mod R coincide if and only if = 0 and .
Full matrix algebras with structure systems
We study associative, basic n × n𝔸-full matrix algebras over a field, whose multiplications are determined by structure systems 𝔸, that is, n-tuples of n × n matrices with certain properties.
Functor categories and group representations
Functors preserving tameness
Galois actions on rings and finite Galois coverings.
Galois coverings and splitting properties of the ideal generated by halflines
Given a locally bounded k-category R and a group acting freely on R we study the properties of the ideal generated by a class of indecomposable locally finite-dimensional modules called halflines (Theorem 3.3). They are applied to prove that under certain circumstances the Galois covering reduction to stabilizers, for the Galois covering F: R → R/G, is strictly full (Theorems 1.5 and 4.2).
Galois coverings and the Clebsch-Gordan problem for quiver representations
We study the Clebsch-Gordan problem for quiver representations, i.e. the problem of decomposing the point-wise tensor product of any two representations of a quiver into its indecomposable direct summands. For this purpose we develop results describing the behaviour of the point-wise tensor product under Galois coverings. These are applied to solve the Clebsch-Gordan problem for the double loop quivers with relations αβ = βα = αⁿ = βⁿ = 0. These quivers were originally studied by I. M. Gelfand and...
Galois coverings and the problem of axiomatization of the representation type of algebras.
Galois coverings of representation-infinite algebras.
General sheaves over weighted projective lines
We develop a theory of general sheaves over weighted projective lines. We define and study a canonical decomposition, analogous to Kac's canonical decomposition for representations of quivers, study subsheaves of a general sheaf, general ranks of morphisms, and prove analogues of Schofield's results on general representations of quivers. Using these, we give a recursive algorithm for computing properties of general sheaves. Many of our results are proved in a more abstract setting, involving a hereditary...
Generalized Brauer tree orders