n-表示有限代数与扭分数Calabi-Yau代数
n-representation-finite algebras and twisted fractionally Calabi-Yau algebras
摘要：
本文从分数Calabi-Yau性质的角度研究了$n$ -表示有限代数。我们将证明所有的$n$ -表示有限代数都是扭曲的分数Calabi-Yau代数。我们还证明了对于任意的$\ell>0$，整体维数至多为$n$的扭$\frac{n(\ell-1)}{\ell}$ -Calabi-Yau代数是$n$ -表示有限的.作为应用，我们给出了利用张量积构造$n$ -表示有限代数的方法。
英文摘要：
In this short paper, we study $n$-representation-finite algebras from the viewpoint of the fractionally Calabi-Yau property. We shall show that all $n$-representation-finite algebras are twisted fractionally Calabi-Yau. We also show that for any $\ell>0$, twisted $\frac{n(\ell-1)}{\ell}$-Calabi-Yau algebras of global dimension at most $n$ are $n$-representation-finite. As an application, we give a construction of $n$-representation-finite algebras using the tensor product.
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