A Z_3-graded generalization of supermatrices
  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. 
Bertrand Le Roy