Nakayama Algebras which are Higher Auslander Algebras
| Autor: | Sen, Emre |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Comments are welcome! v.4 Major revision according to referee report. Main results are same but proofs are elaborated. For linear case, we add new section. v.3 We change the term repetition with covering. CM. Ringel pointed out a bug in thm 1.7. Now, it is fixed by introducing new concept "Nakayama cycle" which is suggested by CM. Ringel. We add more examples |
| Databáze: | arXiv |
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