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

2017/06/26 by Fletcher, James · 2 citations
#46L05 (Primary) 46L08 #46L45 #46L55 (Secondary) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1706.08626

Abstract

In this article we study how decompositions of a quasi-lattice ordered group (G,P) relate to decompositions of the Nica-Toeplitz algebra NT_X and Cuntz-Nica-Pimsner algebra NO_X 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 ℕ^k may be realised as k-times iterated Toeplitz and Cuntz-Pimsner algebras respectively.

Cited by

• Reduced C^*-algebras of Product Systems -- an E₀-semigroup and a Groupoid perspective
• Lifting isomorphisms in K-theory through gradings of C^*-algebras

Related

• Cuntz-Nica-Pimsner algebras associated to product systems over quasi-lattice ordered groupoids
• C*-algebras associated to product systems of Hilbert bimodules
• Cuntz-Nica-Pimsner algebras of product systems over groupoids
• Finite dimensional approximations for Nica-Pimsner algebras
• A uniqueness theorem for the Nica-Toeplitz algebra of a compactly\n aligned product system