Restriction and Extension of Partial Actions

14 Nov 2020 Bagio Dirceu Paques Antonio Pinedo Héctor

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 $A$?.. (read more)

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