We study strong compactly aligned product systems of ℤ ^N₊ over a C*-algebra A. We provide a description of their Cuntz-Nica-Pimsner algebra in terms of tractable relations coming from ideals of A. This approach encompasses product systems where the left action is given by compacts, as well as a wide class of higher rank graphs (beyond row-finite).

Moreover we analyze higher rank factorial languages and their C*-algebras. Many of the rank one results in the literature find here their higher rank analogues. In particular, we show that the Cuntz-Nica-Pimsner algebra of a higher rank sofic language coincides with the Cuntz-Krieger algebra of its unlabeled follower set higher rank graph. However, there are also differences. For example, the Cuntz-Nica-Pimsner can lie in-between the first quantization and its quotient by the compactly supported operators.

我们研究了 ℤ ^N ₊在 C*-代数A 上的强紧致排列的乘积系统。我们根据来自A 的理想的易处理关系描述了他们的 Cuntz-Nica-Pimsner 代数。这种方法包括产品系统，其中左动作由压缩给出，以及广泛的高级图（超出行有限）。

此外，我们分析了更高阶阶乘语言及其 C*-代数。文献中的许多排名第一的结果在这里找到了它们的更高排名的类似物。特别是，我们证明了更高等级的苏菲克语言的 Cuntz-Nica-Pimsner 代数与其未标记的跟随者集更高等级图的 Cuntz-Krieger 代数相吻合。但是，也存在差异。例如，Cuntz-Nica-Pimsner 可以位于第一个量化与其紧支持算子的商之间。