Support $\tau$-tilting modules and semibricks over group graded algebras

Simion Breaz; Andrei Marcus; George Ciprian Modoi

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arXiv · 2209.02992

Support $\tau$-tilting modules and semibricks over group graded algebras

Simion Breaz·Andrei Marcus·George Ciprian Modoi

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Abstract

We consider a finite dimensional strongly $G$-graded algebra $A$ with { self-injective} $1$-component $B$, and in our main result we prove that the induction from $B$ to $A$ of a basic support $\tau$-tilting pair of $B$-modules is a support $\tau$-tilting pair $(M,P)$ of $A$-modules if and only if $M$ is $G$-invariant. A similar statement holds for the restriction from $A$ to $B$, so our results may be viewed as Clifford and Maschke type theorems for $2$-term silting complexes. We also give applications to semibricks and the associated wide subcategories.

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BibTeX RIS

Simion Breaz, Andrei Marcus, George Ciprian Modoi. 2022-09-07. Support $\tau$-tilting modules and semibricks over group graded algebras. https://arxiv.org/abs/2209.02992

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