单壁碳纳米管对称群的线性表示
On the linear representations of the symmetry groups of single-wall carbon nanotubes
摘要：
形成碳纳米管的原子的位置通常通过使用对称群的生成元系统来描述。每个原子位置对应于集合Z x {0，1，.，n} x {0，1}，其中n取决于所考虑的纳米管。我们得到一个替代的，而不同的描述，从一个三轴描述的蜂窝晶格。在我们的数学模型中，它是由集合{（v_0，v_1，v_2）\in Z ^3中的等价关系定义的因子空间|v_0+v_1+v_2 \in {0，1}}，原子位置的邻居可以用更简单的方式描述，具有几何或物理意义的数学对象具有更简单和更对称的形式。我们提出了一些结果，单壁碳纳米管的线性表示，以说明所提出的方法。
英文摘要：
The positions of atoms forming a carbon nanotube are usually described by using a system of generators of the symmetry group. Each atomic position corresponds to an element of the set Z x {0,1,...,n} x {0,1}, where n depends on the considered nanotube. We obtain an alternate rather different description by starting from a three-axes description of the honeycomb lattice. In our mathematical model, which is a factor space defined by an equivalence relation in the set {(v_0,v_1,v_2)\in Z^3 | v_0+v_1+v_2\in {0,1}}, the neighbours of an atomic position can be described in a simpler way, and the mathematical objects with geometric or physical significance have a simpler and more symmetric form. We present some results concerning the linear representations of single-wall carbon nanotubes in order to illustrate the proposed approach.
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