We consider maximal non-l-intertwining collections, which are a higher-dimensional version of the maximal non-crossing collections which give clusters of Plücker coordinates in the Grassmannian coordinate ring, as described by Scott. We extend a method of Scott for producing such collections, which are related to tensor products of higher Auslander algebras of type A. We show that a higher preprojective algebra of the tensor product of two d-representation-finite algebras has a d-precluster-tilting subcategory. Finally, we relate mutations of these collections to a form of tilting for these algebras.

中文翻译：

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A型高等奥兰德代数张量积的组合

我们考虑最大非l- 交织集合，这是最大非交叉集合的更高维版本，它在格拉斯曼坐标环中给出 Plücker 坐标簇，如 Scott 所述。我们扩展了 Scott 的方法来生成此类集合，这些集合与类型的高等 Auslander 代数的张量积有关一种. 我们证明了两个的张量积的更高的预投影代数d-表示有限代数有一个d-precluster-tilting 子类别。最后，我们将这些集合的突变与这些代数的一种倾斜形式联系起来。