Extending (τ-)tilting subcategories and (co)silting modules

Abstract

Assume that B is a finite dimensional algebra, and $A=B[P_0]$ is the one-point extension algebra of B using a finitely generated projective B-module P₀. The categories of B-modules and A-modules are connected via two adjoint functors known as the restriction and extension functors, denoted by $\mathcal{R}$ and $\mathcal{E}$, respectively. These functors have nice homological properties and have been studied in the category $\text{mod-}A$ of finitely presented modules that we extend to the category $\text{Mod-}A$ of all A-modules. Our main focus is to investigate the behavior of important subcategories (tilting and τ-tilting subcategories) and objects (finendo quasi-tilting modules, silting modules, and cosilting modules) under these functors.

KEYWORDS:

• (τ-)tilting subcategories
• (co)silting modules
• cotorsion torsion triples
• one-point extension algebras

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 18E40
• 16S90
• 16E30
• 18G15

Acknowledgments

We would like to thank the referee for her/his insightful comments and hints that improved the presentation of the paper. We also thank Lidia Angeleri Hügel for pointing out the reference [10]. This work was partly done during a visit of the first author to the Institut des Hautes Études Scientifiques (IHES), Paris, France. The first and fourth authors would like to express their gratitude for the support and excellent atmosphere provided at IHES.

Additional information

Funding

The work of the first author is based on research funded by Iran National Science Foundation (INSF) under project No. 4001480. The research of the third author was supported by a grant from IPM. The fourth author is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 893654.