HNN extensions of quasi-lattice ordered groups and their operator algebras

Astrid an Huef; Iain Raeburn; Ilija Tolich

HNN extensions of quasi-lattice ordered groups and their operator algebras

Operator Algebras 2017-03-28 v1

Authors: Astrid an Huef , Iain Raeburn , Ilija Tolich

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.

Keywords

HNN extensions quasi-lattice ordered groups operator algebras Baumslag-Solitar group positive cone amenability

Cite

@article{arxiv.1703.08907,
  title  = {HNN extensions of quasi-lattice ordered groups and their operator algebras},
  author = {Astrid an Huef and Iain Raeburn and Ilija Tolich},
  journal= {arXiv preprint arXiv:1703.08907},
  year   = {2017}
}

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22 pages

HNN extensions of quasi-lattice ordered groups and their operator algebras

Abstract

Keywords

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