تقرير
Full Cuntz-Krieger dilations via non-commutative boundaries
| العنوان: | Full Cuntz-Krieger dilations via non-commutative boundaries |
|---|---|
| المؤلفون: | Dor-On, Adam, Salomon, Guy |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Operator Algebras, Mathematics - Functional Analysis, 47L55, 47A20, 47L75, 47L80 |
| الوصف: | We apply Arveson's non-commutative boundary theory to dilate every Toeplitz-Cuntz-Krieger family of a directed graph $G$ to a full Cuntz-Krieger family for $G$. We do this by describing all representations of the Toeplitz algebra $\mathcal{T}(G)$ that have unique extension when restricted to the tensor algebra $\mathcal{T}_+(G)$. This yields an alternative proof to a result of Katsoulis and Kribs that the $C^*$-envelope of $\mathcal T_+(G)$ is the Cuntz-Krieger algebra $\mathcal O(G)$. We then generalize our dilation results further, to the context of colored directed graphs, by investigating free products of operator algebras. These generalizations rely on results of independent interest on complete injectivity and a characterization of representations with the unique extension property for free products of operator algebras. Comment: Added details in Section 2, and reworking of Section 4 following a remark of Elias Katsoulis. Accepted to J. London Math. Soc |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1112/jlms.12140 |
| URL الوصول: | http://arxiv.org/abs/1702.04308 |
| رقم الأكسشن: | edsarx.1702.04308 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1112/jlms.12140 |
|---|