JournalsdmVol. 23pp. 327–351

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

  • 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

  • Astrid an Huef

    School of Mathematics & Statistics, Victoria University of Wellington, Wellington, New Zealand
HNN Extensions of Quasi-Lattice Ordered Groups and their Operator Algebras cover
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Abstract

The Baumslag-Solitar group is an example of an HNN extension. J. Spielberg [J. Lond. Math. Soc., II. Ser. 86, No. 3, 728–754 (2012; Zbl 1264.46040)] showed that it has a natural positive cone, and that it is then a quasi-lattice ordered group in the sense of A. Nica [J. Oper. Theory 27, No. 1, 17–52 (1992; Zbl 0809.46058)]. We give conditions for an HNN extension of a quasi-lattice ordered group to be quasi-lattice ordered. In that case, if is amenable as a quasi-lattice ordered group, then so is the HNN extension.

Cite this article

Iain Raeburn, Ilija Tolich, Astrid an Huef, HNN Extensions of Quasi-Lattice Ordered Groups and their Operator Algebras. Doc. Math. 23 (2018), pp. 327–351

DOI 10.4171/DM/620