Question: Abstract Lie brackets

Hi Everyone!

The differential geometry packege of Maple allows one to compute Lie brackets of vector fields in coordinates.

I wonder if it is possible to compute Lie brackets in a more abstract fashion. For instance, I wish to define X,Y,Z as elements of a Lie algebra and a,b,c to be constants. For them I want to compute (= expand and simplify) expressions like [[aX+bY,cZ],[cY,[bX+cZ]]] using only basic properties of Lie brackets (skew-symmetry + Jacobi identity), without going to coordinates. Is it possible?



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