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

Simion Breaz; Andrei Marcus; George Ciprian Modoi

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

Representation Theory 2022-11-17 v3 Group Theory Rings and Algebras

Authors: Simion Breaz , Andrei Marcus , George Ciprian Modoi

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.

Keywords

module theory gorenstein-projective modules lie algebras and modules

Cite

@article{arxiv.2209.02992,
  title  = {Support $\tau$-tilting modules and semibricks over group graded algebras},
  author = {Simion Breaz and Andrei Marcus and George Ciprian Modoi},
  journal= {arXiv preprint arXiv:2209.02992},
  year   = {2022}
}

Comments

For v2: An essential hypothesis (i.e. self-injectivity) was added to the main results of the paper

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

Abstract

Keywords

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