On the relation between maximal rigid objects and τ-tilting modules

• Autorzy: Pin Liu , Yunli Xie
• Języki publikacji: EN

Abstrakty

EN

This note compares τ-tilting modules and maximal rigid objects in the context of 2-Calabi-Yau triangulated categories. Let 𝓒 be a 2-Calabi-Yau triangulated category with suspension functor S. Let R be a maximal rigid object in 𝓒 and let Γ be the endomorphism algebra of R. Let F be the functor $Hom_{𝓒}(R,-): 𝓒 → mod Γ$. We prove that any τ-tilting module over Γ lifts uniquely to a maximal rigid object in 𝓒 via F, and in turn, that projection from 𝓒 to mod Γ sends the maximal rigid objects which have no direct summands from add SR to τ-tilting Γ-modules, and in general, that the Γ-modules corresponding to the maximal rigid objects are the support τ-tilting modules.

Kategorie tematyczne

• 18E30: Derived categories, triangulated categories
• 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 142
• Numer: 2
• Strony: 169-178

Daty

wydano

2016

Twórcy

autor

Pin Liu

• Department of Mathematics, Southwest Jiaotong University, 611756 Chengdu, P.R. China

autor

Yunli Xie

• Department of Mathematics, Southwest Jiaotong University, 611756 Chengdu, P.R. China

Identyfikatory

DOI

10.4064/cm142-2-2