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- W2340986906 abstract "Motivated by $tau$-tilting theory developed by Adachi, Iyama and Reiten, for a finite-dimensional algebra $Lambda$ with action by a finite group $G$, we introduce the notion of $G$-stable support $tau$-tilting modules. Then we establish bijections among $G$-stable support $tau$-tilting modules over $Lambda$, $G$-stable two-term silting complexes in the homotopy category of bounded complexes of finitely generated projective $Lambda$-modules, and $G$-stable functorially finite torsion classes in the category of finitely generated left $Lambda$-modules. In the case when $Lambda$ is the endomorphism of a $G$-stable cluster-tilting object $T$ over a Hom-finite 2-Calabi-Yau triangulated category $mathcal{C}$ with a $G$-action, these are also in bijection with $G$-stable cluster-tilting objects in $mathcal{C}$. Moreover, we investigate the relationship between stable support $tau$-tilitng modules over $Lambda$ and the skew group algebra $Lambda G$." @default.
- W2340986906 created "2016-06-24" @default.
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- W2340986906 date "2016-04-02" @default.
- W2340986906 modified "2023-09-27" @default.
- W2340986906 title "G-stable support $tau$-tilting modules" @default.
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