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Im messing around with a Lie 3-Algebra at the moment(Im not sure how widespread these are. They obey similar rules to a Lie Algebra).

I have a bracket that looks like this:

[x1,x2,x3]=c*x0+a*x1+g*x2+h*x3, with c,a,g,h, some structure constants.

I also have the relation a=-g.

Am I allowed to then say [x1,x2,x3]=c*x0+a*x2-g*x2+h*x3

or [x1,x2,x3]=c*x0=h*x3?

I suppose my question amounts to does a=-g also mean a*x^1=-g*x^2?

thanks so much

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# Lie 3-Algebra

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