Heriot-Watt Mathematics Report Series
HWM02-15, 29 Apr 2002
HNN extensions of inverse semigroups and groupoids
N D Gilbert
Abstract
We use the isomorphism between the categories of inverse semigroups and
inductive groupoids to construct HNN extensions of inverse semigroups,
where the associated inverse subsemigroups are order
ideals of the base. Properties of groupoids then ensure that the
base inverse semigroup always embeds in an HNN extension constructed in
this way. Other properties of HNN extensions are determined, including
a description of the maximal subgroups and of the maximal group image,
and the structure of the inverse subsemigroup generated by the stable
letters. Finally, some examples are given.
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