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Actions and partial actions of inductive constellations

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Abstract

Constellations were recently introduced by the authors as one-sided analogues of categories: a constellation is equipped with a partial multiplication for which ‘domains’ are defined but, in general, ‘ranges’ are not. Left restriction semigroups are the algebraic objects modelling semigroups of partial mappings, equipped with local identities in the domains of the mappings. Inductive constellations correspond to left restriction semigroups in a manner analogous to the correspondence between inverse semigroups and inductive groupoids.

In this paper, we define the notions of the action and partial action of an inductive constellation on a set, before introducing the Szendrei expansion of an inductive constellation. Our main result is a theorem which uses this expansion to link the actions and partial actions of inductive constellations, providing a global setting for results previously proved by a number of authors for groups, monoids and other algebraic objects.

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Authors and Affiliations

  1. Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK

    Victoria Gould

  2. Mathematical Institute, 24-29 St. Giles’, Oxford, OX1 3LB, UK

    Christopher Hollings

Authors
  1. Victoria Gould
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  2. Christopher Hollings
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Correspondence to Victoria Gould.

Additional information

Communicated by Francis J. Pastijn.

This work was completed whilst the first author was visiting CAUL, funded by Project ISFL-1-143 of CAUL and Project ‘Semigroups and Languages’ PTDC/MAT/69514/2006. She would like to thank Gracinda Gomes and CAUL for providing a good working environment. The second author acknowledges the support of Project POCTI/0143/2007 of CAUL, financed by FCT and FEDER, and also FCT post-doctoral grant SFRH/BPD/34698/2007.

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Gould, V., Hollings, C. Actions and partial actions of inductive constellations. Semigroup Forum 82, 35–60 (2011). https://doi.org/10.1007/s00233-010-9279-1

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  • DOI: https://doi.org/10.1007/s00233-010-9279-1

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