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5 papers · 2 filters
Projective dimension of modules over cluster-tilted algebras
Louis Beaudet, Thomas Brustle, Gordana Todorov
We study the projective dimension of finitely generated modules over cluster-tilted algebras End(T) where T is a cluster-tilting object in a cluster category C. It is well-known th…
Special biserial algebras with no outer derivations
Ibrahim Assem, Juan Carlos Bustamante, Patrick Le Meur
Let be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of with coefficients in the bimodule vanishes i…
A module-theoretic interpretation of Schiffler's expansion formula
Thomas Brüstle, Jie Zhang
We give a module-theoretic interpretation of Schiffler's expansion formula which is defined combinatorially in terms of complete (T,r)-paths in order to get the expansion of the cl…
Christoffel Words and Markoff Triples: An Algebraic Approach
Alex Lasnier
We introduce a family of modules, called Markoff modules, generated by a cluster-mutation-like iterative process. We show that these modules are combinatorially similar to Christof…
A proof of the strong no loop conjecture
Kiyoshi Igusa, Shiping Liu, Charles Paquette
The strong no loop conjecture states that a simple module of finite projective dimension over an artin algebra has no non-zero self-extension. The main result of this paper establi…