Geodesic
HNN Extensions of Quasi-Lattice Ordered Groups and their Operator Algebras
Documenta mathematica, Tome 23 (2018), pp. 327-351
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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 (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.
DOI : 10.4171/dm/620
Classification : 46L05, 46L55
Mots-clés : amenability, Toeplitz algebras, quasi-lattice order, HNN extension, Baumslag-Solitar groups 
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     title = {HNN {Extensions} of {Quasi-Lattice} {Ordered} {Groups} and their {Operator} {Algebras}},
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Ilija Tolich; Astrid an Huef; Iain Raeburn. HNN Extensions of Quasi-Lattice Ordered Groups and their Operator Algebras. Documenta mathematica, Tome 23 (2018), pp. 327-351. doi: 10.4171/dm/620

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