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arXiv · 1210.8322

ν-stable τ-tilting modules

Yuya Mizuno
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Abstract

Inspired by tau-tilting theory [AIR], we introduce the notion of nu-stable support tau-tilting modules. For any finite dimensional selfinjective algebra Λ, we give bijections between two-term tilting complexes in Kb(proj Λ), nu-stable support tau-tilting Λ-modules and nu-stable functorially finite torsion classes in mod Λ. 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. As an application, we give a necessary condition such that selfinjective algebras are 2-CY tilted.

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Yuya Mizuno. 2013-12-03. ν-stable τ-tilting modules. https://arxiv.org/abs/1210.8322

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