2019/05/06 by Zongzhen Xie, Xie, Zongzhen, Libo Zan +3
Mathematics · Physics and Astronomy · #16E10 #16G10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1905.01871
openalex publication_date 2019/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
τ-rigid modules are essential in the τ-tilting theory introduced by Adachi, Iyama and Reiten. In this paper, we give equivalent conditions for Iwanaga-Gorenstein algebras with self-injective dimension at most one in terms of τ-rigid modules. We show that every indecomposable module over iterated tilted algebras of Dynkin type is τ-rigid. Finally, we give a τ-tilting theorem on homological dimension which is an analog to that of classical tilting modules.