Let A = A(α,β) be a graded down-up algebra with (deg x,deg y) = (1,n) and β≠0, and let ∇A be the Beilinson algebra of A. If n = 1, then a description of the Hochschild cohomology group of ∇A is known. In this paper, we calculate the Hochschild cohomology group of ∇A for the case n ≥ 2. As an application, we see that the structure of the bounded derived category of the noncommutative projective scheme of A is different depending on whether (10) α1β 0 n 10 is zero or not. Moreover, it turns out that there is a difference between the cases n = 2 and n ≥ 3 in the context of Grothendieck groups.

中文翻译：

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Hochschild 上同调与带权重 (1,n) 的分级向下代数有关

让一种 = 一种(α,β)是一个分级向下代数(度 X,度 是的) = (1,n)和β≠0， 然后让∇一种是的贝林森代数一种. 如果n = 1，然后描述 Hochschild 上同调群∇一种是已知的。在本文中，我们计算了 Hochschild 上同调群∇一种对于这种情况n ≥ 2. 作为一个应用，我们看到非交换射影格式的有界派生范畴的结构一种取决于是否 (10) α1β 0 n 10 是否为零。此外，事实证明，案例之间存在差异n = 2和n ≥ 3在格洛腾迪克集团的背景下。