English

Characteristic tilting modules and Ringel duality in the Noetherian world

Representation Theory 2024-05-03 v1 Rings and Algebras

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 AA and BB, we prove that any exact equivalence between the smallest resolving subcategory containing all standard modules over AA and the smallest resolving subcategory containing all standard modules over BB lifts to a Morita equivalence between AA and BB which preserves the quasi-hereditary structure.

Keywords

Cite

@article{arxiv.2405.00729,
  title  = {Characteristic tilting modules and Ringel duality in the Noetherian world},
  author = {Tiago Cruz},
  journal= {arXiv preprint arXiv:2405.00729},
  year   = {2024}
}

Comments

The first part was previously the appendix of the paper arXiv:2208.00291 while the latter part contains parts removed of the second version of the paper arXiv:2210.09344. 26 pages

R2 v1 2026-06-28T16:13:06.610Z