Gröbner-Shirshov bases for the Coxeter groups of the types $G_2,F_4,E_6,E_7$ and $E_8$
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arXiv
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| Format: | Preprint |
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2020
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| author | Pang, Xiaowei Wang, Jun |
| author_facet | Pang, Xiaowei Wang, Jun |
| contents | The author is mainly interest in the Gröbner-Shirshov bases of finite Coxeter groups. It is known that the finite Coxeter groups are classified in terms of Coxeter-Dynkin diagrams. Under the fixed order, it is worth mention that the presentation of group determines the Gröbner-Shirshov bases of group. In this paper, the author rearranges the generators, marks them on Coxeter-Dynkin diagrams, and gets a simple presentation of the Gröbner-Shirshov bases for Coxeter groups of types $G_2, F_4, E_6$ and $E_7$. This article also gives the Gröbner-Shirshov basis of Coxeter group of type $E_8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_07369 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Gröbner-Shirshov bases for the Coxeter groups of the types $G_2,F_4,E_6,E_7$ and $E_8$ Pang, Xiaowei Wang, Jun Group Theory Rings and Algebras 16S15, 20F55 The author is mainly interest in the Gröbner-Shirshov bases of finite Coxeter groups. It is known that the finite Coxeter groups are classified in terms of Coxeter-Dynkin diagrams. Under the fixed order, it is worth mention that the presentation of group determines the Gröbner-Shirshov bases of group. In this paper, the author rearranges the generators, marks them on Coxeter-Dynkin diagrams, and gets a simple presentation of the Gröbner-Shirshov bases for Coxeter groups of types $G_2, F_4, E_6$ and $E_7$. This article also gives the Gröbner-Shirshov basis of Coxeter group of type $E_8$. |
| title | Gröbner-Shirshov bases for the Coxeter groups of the types $G_2,F_4,E_6,E_7$ and $E_8$ |
| topic | Group Theory Rings and Algebras 16S15, 20F55 |
| url | https://arxiv.org/abs/2002.07369 |