ν-Stable τ-Tilting Modules

Abstract

Inspired by τ-tilting theory [3], we introduce the notion of ν-stable support τ-tilting modules. For any finite dimensional selfinjective algebra Λ, we give bijections between two-term tilting complexes in K ^b (proj Λ), ν-stable support τ-tilting Λ-modules, and ν-stable functorially finite torsion classes in modΛ. Moreover, these objects correspond bijectively to selfinjective cluster tilting objects in 𝒞 if Λ is a 2-CY tilted algebra associated with a Hom-finite 2-CY triangulated category 𝒞. We also study some properties of support τ-tilting modules over 2-CY tilted algebras, and we give a necessary condition such that algebras are 2-CY tilted in terms of support τ-tilting modules.

Key Words:

• Cluster tilting
• Selfinjective algebra
• τ-tilting
• Tilting complex

2010 Mathematics Subject Classification:

• 16G10

ACKNOWLEDGMENT

First and foremost, the author would like to thank Osamu Iyama for his support and patient guidance. He is grateful to Kota Yamaura for his kind advice and Takahide Adachi for his valuable comments.

Notes

Communicated by D. Zacharia.