Homological theory of k-idempotent ideals in dualizing varieties

Abstract

In this work, we develop the theory of k-idempotent ideals in the setting of dualizing varieties. Several results given previously by Auslander et al. are extended to this context. Given an ideal $\mathcal{I}$ (which is the trace of a projective module), we construct a canonical recollement which is the analog to a well-known recollement in categories of modules over artin algebras. Moreover, we study the homological properties of the categories involved in such a recollement. Consequently, we find conditions on the ideal $\mathcal{I}$ to obtain quasi-hereditary algebras in such a recollement. Applications to bounded derived categories are also given.

Keywords:

• Dualizing varieties
• functor categories
• ideals
• recollement

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 18A25
• 18E05
• Secondary: 16D90
• 16G10

Acknowledgements

This work presents results obtained during the first author’s doctoral studies, carried out with a CONACYT grant (see [19]). The authors are grateful to the project PAPIIT-Universidad Nacional Autónoma de México IN100520. The authors are grateful for the referee’s valuable comments and suggestions, which have improved the quality and readability of the article.