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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-…
Minimal (-)tilting infinite algebras
Kaveh Mousavand, Charles Paquette
Motivated by a new conjecture on the behavior of bricks, we start a systematic study of minimal -tilting infinite algebras. In particular, we treat minimal -tilting infinite…
-Tilting Finiteness of Non-distributive Algebras and their Module Varieties
Kaveh Mousavand
We treat the -tilting finiteness of those minimal representation-infinite (min-rep-infinite) algebras which are non-distributive. Building upon the new results of Bongartz, we f…
-tilting finiteness of biserial algebras
Kaveh Mousavand
In this paper we treat the -tilting finiteness of biserial (respectively special biserial) algebras over algebraically closed (respectively arbitrary) fields. Inside these famil…