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New York Journal of Mathematics
Volume 24 (2018), 739-814

  

James Fletcher

Iterating the Cuntz-Nica-Pimsner construction for compactly aligned product systems

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Published: September 13, 2018
Keywords: Nica--Toeplitz algebra; Cuntz-Nica-Pimsner algebra; product system.
Subject: Primary: 46L05; Secondary: 46L08, 46L45, 46L55.

Abstract
We study how decompositions of a quasi-lattice ordered group (G,P) relate to decompositions of the Nica-Toeplitz algebra and Cuntz-Nica-Pimsner algebra 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 --- we show that the Nica-Toeplitz algebra and Cuntz-Nica-Pimsner algebra of a compactly aligned product system over Nk may be realised as k-times iterated Toeplitz and Cuntz-Pimsner algebras respectively.

Acknowledgements

This research was supported by an Australian Government Research Training Program (RTP) Scholarship and by the Marsden grant 15-UOO-071 from the Royal Society of New Zealand.


Author information

James Fletcher:
School of Mathematics and Statistics,
Victoria University of Wellington,
Wellington, New Zealand.

james.fletcher@vuw.ac.nz