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arXiv · 1108.5030

Inner coactions, Fell bundles, and abstract uniqueness theorems

S. Kaliszewski·Nadia S. Larsen·John Quigg
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Abstract

We prove gauge-invariant uniqueness theorems with respect to maximal and normal coactions for $C^*$-algebras associated to product systems of $C^*$-correspondences. Our techniques of proof are developed in the abstract context of Fell bundles. We employ inner coactions to prove an essential-inner uniqueness theorem for Fell bundles. As application, we characterise injectivity of homomorphisms on Nica's Toeplitz algebra $\Tt(G, P)$ of a quasi-lattice ordered group $(G, P)$ in the presence of a finite non-trivial set of lower bounds for all non-trivial elements in $P$.

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S. Kaliszewski, Nadia S. Larsen, John Quigg. 2012-05-28. Inner coactions, Fell bundles, and abstract uniqueness theorems. https://arxiv.org/abs/1108.5030

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