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arXiv · 1705.00775

A uniqueness theorem for the Nica-Toeplitz algebra of a compactly aligned product system

James Fletcher
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Abstract

Fowler introduced the notion of a product system: a collection of Hilbert bimodules $\mathbf{X}=\left\{\mathbf{X}_p:p\in P\right\}$ 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. 2017-05-02. A uniqueness theorem for the Nica-Toeplitz algebra of a compactly aligned product system. https://arxiv.org/abs/1705.00775

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