Let $\mathbb K$ be an algebraically closed field. We classify all of the quadratic twisted tensor products $A \otimes_{\tau} B$ in the cases where $(A, B) = (\mathbb K[x], \mathbb K[y])$ and $(A, B) = (\mathbb K[x, y], \mathbb K[z])$. We determine when a quadratic twisted tensor product of this form is Koszul, and when it is Artin–Schelter regular.

中文翻译：

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某些渐变扭曲张量积的分类，Koszulity和Artin-Schelter规律

令$ \ mathbb K $为代数封闭字段。在$（A，B）=（\ mathbb K [x]，\ mathbb K [y]）$和$（ A，B）=（\ mathbb K [x，y]，\ mathbb K [z]）$。我们确定这种形式的二次扭曲张量积何时是Koszul，什么时候是Artin-Schelter正则。