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.
Citation
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
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