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G-stable support τ-tilting modules

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Abstract

Motivated by τ-tilting theory developed by T. Adachi, O. Iyama, I. Reiten, for a finite-dimensional algebra Λ with action by a finite group G; we introduce the notion of G-stable support τ-tilting modules. Then we establish bijections among G-stable support τ-tilting modules over Λ; G-stable two-term silting complexes in the homotopy category of bounded complexes of finitely generated projective Λ-modules, and G-stable functorially finite torsion classes in the category of finitely generated left Λ-modules. In the case when Λ is the endomorphism of a G-stable cluster-tilting object T over a Hom-finite 2-Calabi-Yau triangulated category C with a G-action, these are also in bijection with G-stable cluster-tilting objects in C. Moreover, we investigate the relationship between stable support τ-tilitng modules over Λ and the skew group algebra ΛG

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Yingying Zhang & Zhaoyong Huang

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  1. Yingying Zhang
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  2. Zhaoyong Huang
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Correspondence to Zhaoyong Huang.

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Zhang, Y., Huang, Z. G-stable support τ-tilting modules. Front. Math. China 11, 1057–1077 (2016). https://doi.org/10.1007/s11464-016-0560-9

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  • DOI: https://doi.org/10.1007/s11464-016-0560-9

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