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arXiv · 1909.12215

Restriction and Extension of Partial Actions

Dirceu Bagio·Antonio Paques·Héctor Pinedo
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Abstract

Given a partial action $\alpha=(A_g,\alpha_g)_{g\in \mathcal{G}}$ of a connected groupoid $\mathcal{G}$ on a ring $A$ and an object $x$ of $\mathcal{G}$, the isotropy group $\mathcal{G}(x)$ acts partially on the ideal $A_x$ of $A$ by the restriction of $\alpha$. In this paper we investigate the following reverse question: under what conditions a partial group action of $\mathcal{G}(x)$ on an ideal of $A$ can be extended to a partial groupoid action of $\mathcal{G}$ on $A$? The globalization problem and some applications to the Morita and Galois theories are also considered, as extensions of similar results from the group actions case.

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Dirceu Bagio, Antonio Paques, Héctor Pinedo. 2019-09-26. Restriction and Extension of Partial Actions. https://arxiv.org/abs/1909.12215

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