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HNN extensions of inverse semigroups with zero

Published online by Cambridge University Press:  12 February 2007

E. R. DOMBI  and
N. D. GILBERT
E. R. DOMBI
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS e-mail: [email protected]
N. D. GILBERT
Affiliation:
School of Mathematical and Computer Sciences, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS e-mail: [email protected]
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Abstract

We study a construction of an HNN extension for inverse semigroups with zero. We prove a normal form for the elements of the universal group of an inverse semigroup that is categorical at zero, and use it to establish structural results for the universal group of an HNN extension. Our main application of the HNN construction is to show that graph inverse semigroups –including the polycyclic monoids –admit HNN decompositions in a natural way, and that this leads to concise presentations for them.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 1 , January 2007 , pp. 25 - 39
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

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