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- W4225828122 abstract "We present some generalizations of the well-known correspondence, found by R. Exel, between partial actions of a group $G$ on a set $X$ and semigroup homomorphism of $S(G)$ on the semigroup $I(X)$ of partial bijections of $X,$ being $S(G)$ an inverse monoid introduced by Exel. We show that any unital premorphism $theta:Gto S$, where $S$ is an inverse monoid, can be extended to a semigroup homomorphism $theta^*:Tto S$ for any inverse semigroup $T$ with $S(G)subseteq Tsubseteq P^*(G)times G,$ being $P^*(G)$ the semigroup of non-empty subset of $G$, and such that $E(S)$ satisfies some lattice theoretical condition. We also consider a topological version of this result. We present a minimal Hausdorff inverse semigroup topology on $Gamma(X)$, the inverse semigroup of partial homeomorphism between open subsets of a locally compact Hausdorff space $X$." @default.
- W4225828122 created "2022-05-05" @default.
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- W4225828122 date "2021-12-02" @default.
- W4225828122 modified "2023-09-28" @default.
- W4225828122 title "A topological correspondence between partial actions of groups and inverse semigroup actions" @default.
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