A Z_3-graded generalization of supermatrices
Bertrand Le Roy
TL;DR
This paper introduces Z_3-graded algebraic structures, extending supersymmetric models by defining Z_3-graded Grassmann algebras, matrices, and generalizations of supertrace and superdeterminant.
Contribution
It presents the first systematic development of Z_3-graded algebraic objects, generalizing supermatrices and associated operations.
Findings
Defined Z_3-graded Grassmann algebra
Constructed Z_3-matrices as generalizations of supermatrices
Generalized supertrace and superdeterminant functions
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.
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