标题： 一个 Z_3-分级的超矩阵推广 显示英文标题

标题： A Z_3-graded generalization of supermatrices

摘要： 我们引入了Z₃-分级对象，这是比超对称理论和非交换几何许多模型中使用的更熟悉的Z₂-分级对象的推广。 首先，我们引入Z₃-分级的格拉斯曼代数，并利用这个对象构造了Z₃-矩阵，它们是超矩阵的推广。 然后，我们将超迹和超行列式的概念加以推广。 显示英文摘要

摘要： We introduce Z_3-graded objects which are the generalization of the more familiar Z_2-graded objects that are used in supersymmetric theories and in many models of non-commutative geometry. First, we introduce the Z_3-graded Grassmann algebra, and we use this object to construct the Z_3-matrices, which are the generalizations of the supermatrices. Then, we generalize the concepts of supertrace and superdeterminant.