A Z3-graded generalization of supermatrices

Abstract

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.

A Differential Calculus on the (h, j)-Deformed Z3-Graded Superplane

“…Recently, there have been many attempts to generalize Z 2 -graded constructions to the Z 3 -graded case [ [1], [4], [7], [10], [11], [13], [14]]. Chung [7] studied the Z 3 -graded quantum space that generalizes the Z 2 -graded space called a superspace, using the methods of [18].…”