Let (G; P) be a quasi-lattice ordered group. In this paper we present a modied proof of Laca and Raeburn's theorem about the covariant isometric representations of amenable quasi-lattice ordered groups [7, Theorem 3.7], by following a two stage strategy. First, we construct a universal covariant representation for a given quasi-lattice ordered group (G; P) and show that it is unique. The construction of this object is new; we have not followed either Nica's approach in [10] or Laca and Raeburn's approach in [7], although all three objects are essentially the same. Our approach is a very natural one and avoids some of the intricacies of the other approaches. Then we show if (G; P) is amenable, true representations of (G; P) generate C-algebras which are canonically isomorphic to the universal object.
@article{40511,
title = {C*-algebras generated by isometries and true representations},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {38},
year = {2019},
doi = {10.5269/bspm.v38i5.40511},
language = {EN},
url = {http://dml.mathdoc.fr/item/40511}
}
Ahmed, Mamoon. C*-algebras generated by isometries and true representations. Boletim da Sociedade Paranaense de Matemática, Tome 38 (2019) . doi : 10.5269/bspm.v38i5.40511. http://gdmltest.u-ga.fr/item/40511/