Characteristic tilting modules and Ringel duality in the Noetherian world

2024/04/27 by Tiago Cruz, Cruz, Tiago · 1 citation
Mathematics · #16G30 (Primary) 16D10 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2405.00729

openalex publication_date 2024/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split quasi-hereditary algebras over commutative Noetherian rings are provided. In particular, given two split quasi-hereditary algebras A and B, we prove that any exact equivalence between the smallest resolving subcategory containing all standard modules over A and the smallest resolving subcategory containing all standard modules over B lifts to a Morita equivalence between A and B which preserves the quasi-hereditary structure.

Cited by

• Homological dimensions of Schur algebras S(p,2p) and an Auslander-type correspondence

Related

• Tilting theoretic approach to quasi-hereditary structures
• Ringel duality as an instance of Koszul duality
• Quasi-hereditary algebras via generator-cogenerators of local self-injective algebras and transfer of Ringel duality
• 1-quasi-hereditary algebras: Examples and invariant submodules of\n projectives
• Radically filtered quasi-hereditary algebras and rigidity of tilting\n modules