کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4589756 | 1334904 | 2016 | 52 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Topological aperiodicity for product systems over semigroups of Ore type Topological aperiodicity for product systems over semigroups of Ore type](/preview/png/4589756.png)
We prove a version of uniqueness theorem for Cuntz–Pimsner algebras of discrete product systems over semigroups of Ore type. To this end, we introduce Doplicher–Roberts picture of Cuntz–Pimsner algebras, and the semigroup dual to a product system of ‘regular’ C⁎C⁎-correspondences. Under a certain aperiodicity condition on the latter, we obtain the uniqueness theorem and a simplicity criterion for the algebras in question. These results generalize the corresponding ones for crossed products by discrete groups, due to Archbold and Spielberg, and for Exel's crossed products, due to Exel and Vershik. They also give interesting conditions for topological higher rank graphs and P -graphs, and apply to the new Cuntz C⁎C⁎-algebra QNQN arising from the “ax+bax+b”-semigroup over NN.
Journal: Journal of Functional Analysis - Volume 270, Issue 9, 1 May 2016, Pages 3453–3504