A Z3-graded generalization of supermatrices
نویسنده
چکیده
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 Z3graded Grassmann algebra, and we use this object to construct the Z3matrices, which are the generalizations of the supermatrices. Then, we generalize the concepts of supertrace and superdeterminant.
منابع مشابه
Hypersymmetry: a Z3-graded generalization of Supersymmetry, J.Math.Phys
We propose a generalization of non-commutative geometry and gauge theories based on ternary Z3-graded structures. In the new algebraic structures we define, we leave all products of two entities free, imposing relations on ternary products only. These relations reflect the action of the Z3-group, which may be either trivial, i.e. abc = bca = cab, generalizing the usual commutativity, or non-tri...
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