八元Cayley旋量与E6
Octonionic Cayley Spinors and E6
摘要：
尝试扩展我们以前的工作，使用八元数来描述基本粒子自然导致考虑一个特殊的真实的，非紧形式的特殊李群E6，及其子群。因此，我们导致的描述E6在3x 3的八元数矩阵，推广以前的结果在2x2的情况下。我们的治疗自然包括几个重要的子群E6的描述，特别是G2，F4，和（双覆盖）SO（9，1），这些群体的3-分量的“凯莱旋量”的平方上的行动的解释建议。
英文摘要：
Attempts to extend our previous work using the octonions to describe fundamental particles lead naturally to the consideration of a particular real, noncompact form of the exceptional Lie group E6, and of its subgroups. We are therefore led to a description of E6 in terms of 3x3 octonionic matrices, generalizing previous results in the 2x2 case. Our treatment naturally includes a description of several important subgroups of E6, notably G2, F4, and (the double cover of) SO(9,1), An interpretation of the actions of these groups on the squares of 3-component "Cayley spinors" is suggested.
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