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Ordered groupoids and the holomorph of an inverse semigroup

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Abstract

We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap operation on an inverse semigroup: for groups these two constructions coincide. We present detailed calculations for semilattices of groups and for the polycyclic monoids.

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Acknowledgments

The second author gratefully acknowledges the support of a Summer Vacation Scholarship from the Carnegie Trust for the Universities of Scotland, which made this collaboration possible.

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Authors and Affiliations

  1. School of Mathematical and Computer Sciences and the Maxwell Institute for the Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK

    N. D. Gilbert & E. A. McDougall

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  1. N. D. Gilbert
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  2. E. A. McDougall
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Correspondence to N. D. Gilbert.

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Communicated by Benjamin Steinberg.

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Gilbert, N.D., McDougall, E.A. Ordered groupoids and the holomorph of an inverse semigroup. Semigroup Forum 91, 648–662 (2015). https://doi.org/10.1007/s00233-014-9670-4

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