τ-tilting finite triangular matrix algebras

2020/11/04 by Takuma Aihara, Aihara, Takuma, Takahiro Honma +1
Computer Science · Mathematics · #16B50 #16G20 #16G60 #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2011.02085

openalex publication_date 2020/11/04 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

First, we give a new example of silting-discrete algebras. Second, one explores when the algebra of triangular matrices over a finite dimensional algebra is τ-tilting finite. In particular, we classify algebras over which triangular matrix algebras are τ-tilting finite. Finally, we investigate when a triangular matrix algebra is silting-discrete.

Citations

• Examples of tilting-discrete self-injective algebras which are not silting-discrete

Related

• A characterisation of τ-tilting finite algebras
• Examples of tilting-discrete symmetric algebras
• Silting and Tilting for Weakly Symmetric Algebras
• On τ-tilting finite Borel-Schur algebras
• Examples of tilting-discrete self-injective algebras which are not silting-discrete