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On the globalization of geometric partial (co)modules in the categories of topological spaces and algebras

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Abstract

We study the globalization of partial actions on sets and topological spaces and of partial coactions on algebras by applying the general theory of globalization for geometric partial comodules, as previously developed by the authors. We show that this approach does not only allow to recover all known results in these settings, but it allows to treat new cases of interest, too.

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Notes

  1. The prefix ‘algebraic’ is not standard in literature, but we use it here to distinguish these objects from geometric partial comodule algebras as introduced above.

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Acknowledgements

PS is a Chargé de Recherches of the Fonds de la Recherche Scientifique - FNRS and a member of the National Group for Algebraic and Geometric Structures and their Applications (GNSAGA-INdAM). JV thanks the FNRS (National Research Fund of the French speaking community in Belgium) for support via the MIS project ‘Antipode’ (Grant F.4502.18) and the FWB (fédération Walonie-Bruxelles) for support through the ARC project "from algebra to combinatorics, and back”. The authors express their gratitude to the anonymous referees for the careful reading of this paper and the useful suggestions.

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  1. Département de Mathématique, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050, Brussels, Belgium

    Paolo Saracco & Joost Vercruysse

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  1. Paolo Saracco
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  2. Joost Vercruysse
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Correspondence to Paolo Saracco.

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Communicated by Mark V. Lawson.

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Saracco, P., Vercruysse, J. On the globalization of geometric partial (co)modules in the categories of topological spaces and algebras. Semigroup Forum 105, 534–550 (2022). https://doi.org/10.1007/s00233-022-10269-3

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  • DOI: https://doi.org/10.1007/s00233-022-10269-3

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