Iterating the Cuntz-Nica-Pimsner construction for product systems

In this thesis we study how decompositions of a quasi-lattice ordered group (G; P) relate to decompositions of the Nica-Toeplitz algebra NTX and Cuntz-Nica-Pimsner algebra NOX of a compactly aligned product system X over P. In particular, we are interested in the situation where (G; P) may be realised as the semidirect product of quasi-lattice ordered groups. Our results generalise Deaconu's work on iterated Toeplitz and Cuntz-Pimsner algebras [13]. As a special case we consider when P = Nk and X is the product system associated to a finitely aligned higher-rank graph, and Nk is decomposed as Nk-1xN.