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• W2732037516 abstract "We use product systems of $C^*$-correspondences to introduce twisted $C^*$-algebras of topological higher-rank graphs. We define the notion of a continuous $mathbb{T}$-valued $2$-cocycle on a topological higher-rank graph, and present examples of such cocycles on large classes of topological higher-rank graphs. To every proper, source-free topological higher-rank graph $Lambda$, and continuous $mathbb{T}$-valued $2$-cocycle $c$ on $Lambda$, we associate a product system $X$ of $C_0(Lambda^0)$-correspondences built from finite paths in $Lambda$. We define the twisted Cuntz--Krieger algebra $C^*(Lambda,c)$ to be the Cuntz--Pimsner algebra $mathcal{O}(X)$, and we define the twisted Toeplitz algebra $mathcal{T} C^*(Lambda,c)$ to be the Nica--Toeplitz algebra $mathcal{NT}(X)$. We also associate to $Lambda$ and $c$ a product system $Y$ of $C_0(Lambda^infty)$-correspondences built from infinite paths. We prove that there is an embedding of $mathcal{T} C^*(Lambda,c)$ into $mathcal{NT}(Y)$, and an isomorphism between $C^*(Lambda,c)$ and $mathcal{O}(Y)$." @default.
• W2732037516 created "2017-07-14" @default.
• W2732037516 creator A5037086637 @default.
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• W2732037516 date "2018-10-01" @default.
• W2732037516 modified "2023-09-24" @default.
• W2732037516 title "Product-system models for twisted C⁎-algebras of topological higher-rank graphs" @default.
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• W2732037516 doi "https://doi.org/10.1016/j.jmaa.2018.06.052" @default.
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