Actions and partial actions of inductive constellations

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Publication details

JournalSemigroup Forum
DateE-pub ahead of print - 4 Dec 2010
DatePublished (current) - Nov 2011
Issue number1
Volume82
Number of pages26
Pages (from-to)35-60
Early online date4/12/10
Original languageEnglish

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.

    Research areas

  • Algebra

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