群论方法构建石墨烯
Group theoretical methods to construct the graphene
摘要：
在本文中，我们将这种在欧氏平面上镶嵌的顶点被碳原子占据的正六边形称为石墨烯。我们描述了六种不同的方法来生成石墨烯的群论的手段。从李代数$A_2$和$G_2$的三角格出发有两种方法，而对于$B_3$、$C_3$和$A_3$中的每一个，通过将它们的最低表示的权系统投影到$A_2$的六边形上有一种方法。呈现石墨烯的着色。从一种颜色变为另一种颜色称为相变。描述了石墨烯的多步细化。
英文摘要：
In this paper, the tiling of the Euclidean plane with regular hexagons whose vertices are occupied by carbon atoms is called the graphene. We describe six different ways to generate the graphene by the means of group theory. There are two ways starting from the triangular lattice of Lie algebra $A_2$ and $G_2$, and one way for each of the Lie algebras $B_3$, $C_3$ and $A_3$, by projecting the weight system of their lowest representation to the hexagons of $A_2$. Colouring of the graphene is presented. Changing from one colouring to another is called phase transition. Multistep refinements of the graphene are described.
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