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september 2022 Galois correspondence for group-type partial actions of groupoids
Dirceu Bagio, Alveri Sant'Ana, Thaísa Tamusiunas
Bull. Belg. Math. Soc. Simon Stevin 28(5): 745-767 (september 2022). DOI: 10.36045/j.bbms.210807

Abstract

Let $G$ be a finite groupoid and $\alpha=(S_g,\alpha_g)_{g\in G}$ a unital partial action of group-type of $G$ on a commutative ring $S=\oplus_{y\in G_0}S_y$. We prove a Galois correspondence between a class of wide subgroupoids of $G$ 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. "Galois correspondence for group-type partial actions of groupoids." Bull. Belg. Math. Soc. Simon Stevin 28 (5) 745 - 767, september 2022. https://doi.org/10.36045/j.bbms.210807

Information

Published: september 2022
First available in Project Euclid: 16 September 2022

Digital Object Identifier: 10.36045/j.bbms.210807

Subjects:
Primary: 16W22 , 18B40
Secondary: 20L05

Keywords: Galois theory , groupoid , Group-type partial action

Rights: Copyright © 2022 The Belgian Mathematical Society

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Vol.28 • No. 5 • september 2022
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