Finite-dimensional approximations for Nica–Pimsner algebras
Finite-dimensional approximations for Nica–Pimsner algebras
复制标题
Nica-Pimsner 代数的有限维近似
DOI：
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发表时间：
2019
影响因子：
0.9
通讯作者：
E. Kakariadis
中科院分区：
文献类型：
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作者：
E. Kakariadis
给出了一类拟格序群的Cuntz-Nica-Pimsner代数有核的充要条件。首先，我们处理自由交换格的情况。我们用这个作为垫脚石，以解决产品系统的准格控制的自由阿贝尔格，并满足极小性质。我们的设置可以容纳像Baumslag-Solitar格（n=m>0）和直角Artin群这样的例子。更一般地说，我们的结果适用的类准格是封闭的下采取半直接和图的产品。在这个过程中，我们做得更多。我们的论点解决了Nica-Pimsner代数，该代数承认对小不动点代数的忠实条件期望和系数代数的忠实副本。这是介于Toeplitz-Nica-Pimsner代数和Cuntz-Nica-Pimsner代数之间的CNP-相对代数的情况。我们完成了这项研究的相关结果的正确性。
We give necessary and sufficient conditions for nuclearity of Cuntz–Nica–Pimsner algebras for a variety of quasi-lattice ordered groups. First we deal with the free abelian lattice case. We use this as a stepping-stone to tackle product systems over quasi-lattices that are controlled by the free abelian lattice and satisfy a minimality property. Our setting accommodates examples like the Baumslag–Solitar lattice for $n=m>0$ and the right-angled Artin groups. More generally, the class of quasi-lattices for which our results apply is closed under taking semi-direct and graph products. In the process we accomplish more. Our arguments tackle Nica–Pimsner algebras that admit a faithful conditional expectation on a small fixed point algebra and a faithful copy of the coefficient algebra. This is the case for CNP-relative quotients in-between the Toeplitz–Nica–Pimsner algebra and the Cuntz–Nica–Pimsner algebra. We complete this study with the relevant results on exactness.