Brick-directed algebras are exactly the algebras whose torsion-class lattice is left modular, extremal, or trim; the wall-and-chamber and Newton-polytope reformulations follow.
Asai, Mutations of simple-minded collections and -tilting reduction (in preparation)
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Brick-splitting Torsion Pairs and Left Modularity
Brick-directed algebras are exactly the algebras whose torsion-class lattice is left modular, extremal, or trim; the wall-and-chamber and Newton-polytope reformulations follow.