A Z_3-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.

Cited by in corpus (3)

• Hypersymmetry: a Z_3-graded generalization of supersymmetry
• Differential geometry of the Z_3-graded quantum superplane
• The Hopf algebra structure of the Z${}_3$-graded quantum supergroup GL${}_{q,j}(1|1)$