A BRICK VERSION OF A THEOREM OF AUSLANDER. (5th March 2023)

• Record Type: Journal Article
• Authors: SENTIERI, FRANCESCO
• Is Part Of: Nagoya mathematical journal. Volume 249(2023)
• Page Start: 88
• Page End: 106
• Publication Date: 2023-03-05
• Subjects: 16G20 -- 18E40; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathematics; Wiskunde; Electronic journals; Periodicals; 510.5
• DOI: 10.1017/nmj.2022.22
• Languages: English
• ISSNs: 0027-7630

Abstract

Abstract: We prove that a finite-dimensional algebra $ \Lambda $ is $ \tau $ -tilting finite if and only if all the bricks over $ \Lambda $ are finitely generated. This is obtained as a consequence of the existence of proper locally maximal torsion classes for $ \tau $ -tilting infinite algebras.