Finding a cluster-tilting object for a representation finite cluster-tilted algebra
We provide a technique to find a cluster-tilting object having a given cluster-tilted algebra as endomorphism ring in the finite type case.
M. A. Bertani-Økland, S. Oppermann, A. Wrålsen (2010)
Colloquium Mathematicae
We provide a technique to find a cluster-tilting object having a given cluster-tilted algebra as endomorphism ring in the finite type case.
E. Cline, B. Parshall, L. Scott (1988)
Journal für die reine und angewandte Mathematik
Claus Michael Ringel (1978)
Mathematische Zeitschrift
Leonid F. Barannyk (2012)
Colloquium Mathematicae
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...
Leonid F. Barannyk, Dariusz Klein (2012)
Colloquium Mathematicae
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...
Hermund André Torkildsen (2011)
Colloquium Mathematicae
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.
Leonid F. Barannyk (2010)
Colloquium Mathematicae
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.
Otto Kerner, Andrzej Skowroński, Kunio Yamagata, Dan Zacharia (2004)
Open Mathematics
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...
Enochs, E., Estrada, S., García Rozas, J.R., Oyonarte, L. (2003)
International Journal of Mathematics and Mathematical Sciences
Robert Wisbauer (1980)
Mathematische Zeitschrift
Ibrahim Assem, Dan Zacharia (1999)
Colloquium Mathematicae
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 .
Hisaaki Fujita (2003)
Colloquium Mathematicae
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.
Green, J.A. (1985/1986)
Portugaliae mathematica
J. de la Peña (1991)
Fundamenta Mathematicae
M. Auslander, I. Reiten, S.O. Smalo (1989)
Mathematica Scandinavica
Piotr Dowbor (2004)
Colloquium Mathematicae
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).
Martin Herschend (2007)
Colloquium Mathematicae
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...
Stanislaw Kasjan, José Antonio de la Peña (2005)
Extracta Mathematicae
Andrzej Skowronski, Piotr Dowbor (1987)
Commentarii mathematici Helvetici
William Crawley-Boevey (2008)
Colloquium Mathematicae
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...