Partial actions: Restriction and Globalization
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Författare
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Modellbyggare
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Sammanfattning
Partial actions generalize group actions by allowing the domain of the maps induced
by each group element to be subspaces rather than the entire space. Often, partial
actions arise from restricting a global action to a subspace, which means they are
globalizable. It is a good question to ask whether every partial action is globalizable.
In the category of sets, every partial action admits a unique globalization. In
the topological setting, however, some properties may be lost in the globalization
process. That is, a topological partial action on a Hausdorff space may have an
enveloping action that is not Hausdorff. Moreover, a special class of partial actions
of a finite group, those with the decomposition property, are guaranteed to have a
Hausdorff enveloping space.
Beskrivning
Ämne/nyckelord
partial action. globalization, Hausdorff space, decomposition property.