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

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Liu P., Xie Y.

Colloquium Mathematicum

2016

tom 142

nr 2

169-178

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Liu P.

1 Xie Y.

1 2016

Wyniki wyszukiwania

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