A Z3-graded generalization of supermatrices
Bertrand Le Roy
Abstract
We introduce Z3-graded objects which are the generalization of the more familiar Z2-graded objects that are used in supersymmetric theories and in many models of non-commutative geometry. First, we introduce the Z3-graded Grassmann algebra, and we use this object to construct the Z3-matrices, which are the generalizations of the supermatrices. Then, we generalize the concepts of supertrace and superdeterminant.
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