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I just read through a paper on a [math]\mathbb{Z} _ 3[/math] graded Algebra. In this instance we are talking about color Dirac spinors in space-time. It looks like the author is talking about [math]\left ( SU(3) \otimes L^4 \otimes \mathbb{Z}_2 \otimes \mathbb{Z} _2 \right ) \otimes \mathbb{Z} _3[/math]. ( SU(3) is the color group, [math]L_4 [/math] is the Lorentz group, [math]\mathbb{Z} _2 \otimes \mathbb{Z} _2[/math] is the Dirac 4-spinor group, and [math]\mathbb{Z} _3[/math] is the usual group on 3 elements.
I can (mostly) follow the paper assuming the tensor products, but what do they mean by the word "graded?"
Thanks!
-Dan
I can (mostly) follow the paper assuming the tensor products, but what do they mean by the word "graded?"
Thanks!
-Dan