9 papers
A Proof of the Second brick-Brauer-Thrall Conjecture for -infinite algebras
Kaveh Mousavand, Charles Paquette
For any finite-dimensional algebra over an algebraically closed field, we prove that if is -infinite, then the Second brick-Brauer-Thrall Conjecture holds for . In fa…
Brick infinite algebras admit infinitely many non--rigid bricks
Kaveh Mousavand, Charles Paquette
For finite dimensional algebras over algebraically closed fields, we settle a question previously known only for certain families of algebras. More specifically, motivated by some…
Left modularity and extremality for (some) infinite lattices
Sota Asai, Osamu Iyama, Kaveh Mousavand +1
For some important families of complete infinite lattices, we study some generalizations of two fundamental notions which are mostly treated for finite lattices. Specifically, for…
Infinite string bricks and Sturmian words over some gentle algebras
Mark Deaconu, Kaveh Mousavand, Charles Paquette
We study infinite string modules that are bricks over some gentle algebras. In particular, we first give a complete classification of these modules over the double-Kronecker gentle…
On the bricks (Schur representations) of finite dimensional algebras
Kaveh Mousavand, Charles Paquette
This manuscript treats the diverse applications of bricks within modern representation theory and several related domains, and reviews the recent developments and new results on br…
Brick-splitting Torsion Pairs and Left Modularity
Sota Asai, Osamu Iyama, Kaveh Mousavand +1
We introduce the notion of brick-splitting torsion pairs as a modern analogue and generalization of the classical notion of splitting torsion pairs. A torsion pair is called brick-…
Categories of generalized thread quivers
Charles Paquette, Job Daisie Rock, Emine Yıldırım
We study the representation category of thread quivers and their quotients. A thread quiver is a quiver in which some arrows have been replaced by totally ordered sets. Pointwise f…
Hom-orthogonal modules and brick-Brauer-Thrall conjectures
Kaveh Mousavand, Charles Paquette
For finite dimensional algebras over algebraically closed fields, we study the sets of pairwise Hom-orthogonal modules and obtain new results on some open conjectures on the behavi…
Geometric interactions between bricks and -rigidity
Kaveh Mousavand, Charles Paquette
For finite-dimensional algebras over algebraically closed fields, we consider two fundamental classes of modules and their geometric counterparts: bricks and -rigid modules, as…