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arXiv · 2108.01180

Galois correspondence for group-type partial actions of groupoids

Dirceu Bagio·Alveri Sant'Ana·Thaísa Tamusiunas
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Abstract

Let $\operatorname{G}$ be a finite groupoid and $\alpha=(S_g,\alpha_g)_{g\in \operatorname{G}}$ a unital partial action of group-type of $\operatorname{G}$ on a commutative ring $S=\oplus_{y\in\operatorname{G}_0}S_y$. We shall prove a Galois correspondence between a class of wide subgroupoids of $\operatorname{G}$ and a class of subrings of $S$. We recover known results for global groupoid actions and we give several examples to illustrate the correspondence.

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Dirceu Bagio, Alveri Sant'Ana, Thaísa Tamusiunas. 2021-08-02. Galois correspondence for group-type partial actions of groupoids. https://arxiv.org/abs/2108.01180

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