Coxeter群G₂,F₄,E₆,E₇和E₈的Gröbner-Shirshov基
Gröbner-Shirshov bases for the Coxeter groups of the types $G_2,F_4,E_6,E_7$ and $E_8$
AI总结：
本文研究Coxeter群G₂,F₄,E₆,E₇和E₈的Gröbner-Shirshov基，通过重新排列生成元并标记Coxeter-Dynkin图，获得简洁的基表示。
摘要：
作者主要研究有限Coxeter群的Gröbner-Shirshov基。已知有限Coxeter群通过Coxeter-Dynkin图分类。在固定顺序下，群的呈现决定了群的Gröbner-Shirshov基。本文中，作者重新排列生成元，将其标记在Coxeter-Dynkin图上，并获得了Coxeter群G₂,F₄,E₆和E₇的Gröbner-Shirshov基的简单表示。本文还给出了Coxeter群E₈的Gröbner-Shirshov基。
英文摘要：
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 $E_8$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
