11. HNN Extensions of Quasi-Lattice Ordered Groups and their Operator Algebras

  • Astrid an Huef School of Mathematics & Statistics; Victoria University of Wellington; Wellington, New Zealand
  • Iain Raeburn School of Mathematics & Statistics, Victoria University of Wellington, Wellington, New Zealand
  • Ilija Tolich Dept. of Mathematics & Statistics, University of Otago, Dunedin, New Zealand
Keywords: Toeplitz algebras, quasi-lattice order, HNN extension, Baumslag-Solitar groups, amenability

Abstract

The Baumslag-Solitar group is an example of an HNN extension.
Spielberg showed that it has a natural positive cone, and that it is then a quasi-lattice ordered group in the sense of Nica. We give conditions for an HNN extension of a quasi-lattice ordered group $(G,P)$ to be quasi-lattice ordered. In that case,  if $(G,P)$ is  amenable  as a quasi-lattice ordered group, then so is the HNN extension.

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Published
2018-05-15
Section
Unassigned Articles