Cuntz-Nica-Pimsner algebras of product systems over groupoids

2023/12/18 by Amini, Massoud, Moosazadeh, Mahdi
#46L05 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2312.10923

Abstract

Let X be a product system over a quasi-lattice ordered groupoid (G,P). Under mild hypotheses, we associate to X a C^*-algebra which is couniversal for injective Nica covariant Toeplitz representations of X which preserve the gauge coaction. When (G,P) is a quasi-lattice ordered group this couniversal C^*-algebra coincides with the Cuntz-Nica-Pimsner algebra introduced by Carlsen-Larsen-Sims-Vittadello, and under some mild amenability conditions with that of Sims and Yeend. We prove related gauge invariant uniqueness theorems in this general setup.

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