Geodesic
HNN Extensions of Quasi-Lattice Ordered Groups and their Operator Algebras
Documenta mathematica, Tome 23 (2018), pp. 327-351.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 46L55, 46L05
Keywords: Toeplitz algebras, quasi-lattice order, HNN extension, Baumslag-Solitar groups, amenability 
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an Huef, Astrid; Raeburn, Iain; Tolich, Ilija. HNN Extensions of Quasi-Lattice Ordered Groups and their Operator Algebras. Documenta mathematica, Tome 23 (2018), pp. 327-351. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a52/