Coverings of Laura Algebras: the Standard Case (2010)
Assem, Ibrahim, Bustamante, Juan Carlos, Le Meur, Patrick
In this paper, we study the covering theory of laura algebras. We prove that if a connected laura algebra is standard (that is, it is not quasi-tilted of canonical type and its connecting components...
Coverings of Laura Algebras: the Standard Case (2010)
Assem, Ibrahim, Bustamante, Juan Carlos, Le Meur, Patrick
In this paper, we study the covering theory of laura algebras. We prove that if a connected laura algebra is standard (that is, it is not quasi-tilted of canonical type and its connecting components...
Assem, Ibrahim, Reutenauer, Christophe, Smith, David
Each acyclic graph, and more generally, each acyclic orientation of the graph associated to a Cartan matrix, allows to define a so-called frise; this is a collection of sequences over the positive...
Gentle algebras arising from surface triangulations (2009)
Assem, Ibrahim, Brüstle, Thomas, Charbonneau-Jodoin, Gabrielle, Plamondon, Pierre-Guy
In this paper, we associate an algebra A(T) to a triangulation T of a surface S with a set of boundary marking points. This algebra A(T) is gentle and Gorenstein of dimension one. We also prove that...
ALGEBRAS GIVEN BY LABELLED QUIVERS (2008)
In [3], Bautista and Salmeron explained how, given a finite quiver Z without double arrows or oriented cycles, certain sets of subsets of ZZ (called (P)-generating systems) may, under appropriate...
Coverings of Laura Algebras: the Standard Case (2008)
Assem, Ibrahim, Bustamante, Juan Carlos, Meur, Patrick Le
In this paper, we study the covering theory of laura algebras. We prove that if a connected laura algebra is standard (that is, it is not quasi-tilted of canonical type and its connecting components...
Coverings of Laura Algebras: the Standard Case (2008)
Assem, Ibrahim, Bustamante, Juan Carlos, Le Meur, Patrick
In this paper, we study the covering theory of laura algebras. We prove that if a connected laura algebra is standard (that is, it is not quasi-tilted of canonical type and its connecting components...
Coverings of Laura Algebras: the Standard Case (2008)
Assem, Ibrahim, Bustamante, Juan Carlos, Le Meur, Patrick
In this paper, we study the covering theory of laura algebras. We prove that if a connected laura algebra is standard (that is, it is not quasi-tilted of canonical type and its connecting components...
The first Hochschild cohomology group of a schurian cluster-tilted algebra (2007)
Assem, Ibrahim, Redondo, Maria Julia
Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH^1(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also...
On the Galois coverings of a cluster-tilted algebra (2007)
Assem, Ibrahim, Bruestle, Thomas, Schiffler, Ralf
We study the module category of a certain Galois covering of a cluster-tilted algebra which we call the cluster repetitive algebra. Our main result compares the module categories of the cluster...
Cluster-tilted algebras and slices (2007)
Assem, Ibrahim, Bruestle, Thomas, Schiffler, Ralf
We give a criterion allowing to verify whether or not two tilted algebras have the same relation-extension (thus correspond to the same cluster-tilted algebra). This criterion is in terms of a...
Mutation classes of skew-symmetric 3x3-matrices (2006)
Assem, Ibrahim, Blais, Martin, Brüstle, Thomas, Samson, Audrey
In this paper, we establish a bijection between the set of mutation classes of mutation-cyclic skew-symmetric integral 3x3-matrices and the set of triples of integers (a,b,c) which are all greater...
Cluster-tilted algebras as trivial extensions (2006)
Assem, Ibrahim, Brüstle, Thomas, Schiffler, Ralf
Given a finite dimensional algebra $C$ (over an algebraically closed field) of global dimension at most two, we define its relation-extension algebra to be the trivial extension $C\ltimes...
Cluster categories and duplicated algebras (2005)
Assem, Ibrahim, Brüstle, Thomas, Schiffler, Ralf, Todorov, Gordana
Let $A$ be a hereditary algebra. We construct a fundamental domain for the cluster category of $A$ inside the category of modules over the duplicated algebra $\bar{A}$ of $A$. We then prove that...
The left part and the Auslander-Reiten components of an artin algebra (2005)
Assem, Ibrahim, Cappa, Juan Ángel, Platzeck, María Inés, Trepode, Sonia
Abelian exact subcategories closed under predecessors (2004)
Assem, Ibrahim, Saorin, Manuel
In the category of finitely generated modules over an artinian ring, we classify all the abelian exact subcategories closed under predecessors or, equivalently, all the split torsion pairs with...
Iterated tilted algebras--[microform] /--by Ibrahim Ali Assem. (1982)
Thesis (Ph. D.)--Carleton University, 1981.