Homological theory of $k$-idempotent ideals in dualizing varieties
Category Theory
2021-06-04 v2 Representation Theory
Abstract
In this work, we develop the theory of -idempotent ideals in the setting of dualizing varieties. Several results given previously in \cite{APG} by M. Auslander, M. I. Platzeck, and G. Todorov are extended to this context. Given an ideal (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 to obtain quasi-hereditary algebras in such a recollement. Applications to bounded derived categories are also given.
Keywords
Cite
@article{arxiv.2008.07158,
title = {Homological theory of $k$-idempotent ideals in dualizing varieties},
author = {Luis Gabriel Rodríguez Valdés and Valente Santiago Vargas and Martha Lizbeth Shaid Sandoval Miranda},
journal= {arXiv preprint arXiv:2008.07158},
year = {2021}
}