标题： 超对称性：超对称性的Z_3-分级广义化 显示英文标题

标题： Hypersymmetry: a Z_3-graded generalization of supersymmetry

摘要： 我们提出了一种非交换几何和规范理论的推广，基于三元 Z_3-分级结构。在我们定义的新代数结构中，我们使两个实体的所有乘积保持自由，仅对三元乘积施加关系。这些关系反映了 Z_3-群的作用，该作用可以是平凡的，即 abc = bca = cab，推广了通常的交换性；也可以是非平凡的，即 abc = j*bca，其中 j = e^{(2\pi i)/3}。通常的 Z_2-分级结构如格拉斯曼、李和克利福德代数被推广到 Z_3-分级情形。关于这些新结构最终在基本粒子物理中的可能应用，提出了一些看法。 显示英文摘要

摘要： We propose a generalization of non-commutative geometry and gauge theories based on ternary Z_3-graded structures. In the new algebraic structures we define, we leave all products of two entities free, imposing relations on ternary products only. These relations reflect the action of the Z_3-group, which may be either trivial, i.e. abc=bca=cab, generalizing the usual commutativity, or non-trivial, i.e. abc=jbca, with j=e^{(2\pi i)/3}. The usual Z_2-graded structures such as Grassmann, Lie and Clifford algebras are generalized to the Z_3-graded case. Certain suggestions concerning the eventual use of these new structures in physics of elementary particles are exposed.