8 papers
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…
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…
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…
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-…
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…