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2019 A uniqueness theorem for the Nica--Toeplitz algebra of a compactly aligned product system
James Fletcher
Rocky Mountain J. Math. 49(5): 1563-1594 (2019). DOI: 10.1216/RMJ-2019-49-5-1563

Abstract

Fowler introduced the notion of a product system: a collection of Hilbert bimodules $\mathbf {X}=\{\mathbf {X}_p:p\in P\}$ indexed by a semigroup $P$, endowed with a multiplication implementing isomorphisms $\mathbf {X}_p\otimes _A \mathbf {X}_q\cong \mathbf {X}_{pq}$. When $P$ is quasi-lattice ordered, Fowler showed how to associate a $C^*$-algebra $\mathcal {NT}_\mathbf {X}$ to $\mathbf {X}$, generated by a universal representation satisfying some covariance condition. In this article we prove a uniqueness theorem for these so called Nica–Toeplitz algebras.

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James Fletcher. "A uniqueness theorem for the Nica--Toeplitz algebra of a compactly aligned product system." Rocky Mountain J. Math. 49 (5) 1563 - 1594, 2019. https://doi.org/10.1216/RMJ-2019-49-5-1563

Information

Published: 2019
First available in Project Euclid: 19 September 2019

zbMATH: 07113699
MathSciNet: MR4010573
Digital Object Identifier: 10.1216/RMJ-2019-49-5-1563

Subjects:
Primary: 46L05
Secondary: 46L08, 46L55

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 5 • 2019
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