A BRICK VERSION OF A THEOREM OF AUSLANDER. (5th March 2023) - SENTIERI, FRANCESCO
Abstract: We prove that a finite-dimensional algebra $ Λ $ is $ τ $ -tilting finite if and only if all the bricks over $ Λ $ are finitely generated. This is obtained as a consequence of the existence of proper locally maximal torsion classes for $ τ $ -tilting infinite algebras.