论文标题
中山代数是较高的澳大利亚代数
Nakayama Algebras which are Higher Auslander Algebras
论文作者
论文摘要
我们证明，通过逆转Syzygy滤过过程，可以从较小等级的Nakayama代数构建的任何较高的Auslander代数的循环中山代数。这创建了高级澳大利亚代数的链条，最高为$ \ boldsymbol \ varepsilon $ - 等效。因此，较高的auslander代数的所有环状中山代数的分类减少了线性分类。我们给出了两个应用：对于任何整数$ k $，其中$ 2 \ leq k \ leq 2n-2 $，有一个nakayama代数为等级$ n $，这是全球尺寸$ k $的较高的auslander代数，并且可能是较高的nakayama代数的全球全球维度值的可能值 $\left\{2,\ldots,2n-2\right\}\setminus\left\{n-1\right\}$ if $n$ is even and $\left\{2,\ldots,2n-2\right\}\setminus\left\{ 2,n-1\right\}$ if $n$ is odd.
We prove that any cyclic Nakayama algebra which is a higher Auslander algebra can be uniquely constructed from Nakayama algebras of smaller ranks by reversing the syzygy filtration process. This creates chains of higher Auslander algebras upto $\boldsymbol\varepsilon$-equivalences. Therefore, the classification of all cyclic Nakayama algebras which are higher Auslander algebras reduces to the classification of linear ones. We give two applications of this: for any integer $k$ where $2\leq k\leq 2n-2$, there is a Nakayama algebra of rank $n$ which is a higher Auslander algebra of global dimension $k$ and the possible values of the global dimensions of cyclic Nakayama algebras which are higher Auslander algebras form the sets $\left\{2,\ldots,2n-2\right\}\setminus\left\{n-1\right\}$ if $n$ is even and $\left\{2,\ldots,2n-2\right\}\setminus\left\{ 2,n-1\right\}$ if $n$ is odd.
