Hello. I'm computing a Lie bracket commutation [Xi, Xj] = C_{i,j}^{k} X_{k} = - [Xi, Xj], i,j = 1, ... , 6 and i<j.
and the structural constant C_{i,j}^{k} (ie a mathematical expression or numerical value). For example the following are some of the outputs:
[X4,X5] = (3 E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( Sqrt[3])) (-1 + E^(( 2 t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/Sqrt[ 3])) \8[Theta] ) X3

[X4,X6] = (3 E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( Sqrt[3])) (1 + E^(( 2 t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/Sqrt[ 3])) / 8[Theta]\[Kappa]) X3

[X2,X5] =  f$54648[1] X1 +  f$54648[2] X2 + 2 \[Theta] Sqrt[\[Kappa]] - 
            Sqrt[3] x Sqrt[8 \[Theta] + (3 \[Kappa]]) c$48559[2, 5, 1] + 
        1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]]) E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
           2 Sqrt[3]))) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] +
             Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$48559[2, 5, 2])  X2

 [X2,X6] =  f$52039[1] X1 +  f$52039[2]  X2 + u (-((3 E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(  2 Sqrt[3])) - (t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/ Sqrt[3]) (-1 + E^(( t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/Sqrt[ 3]))^2 (3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] -  Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]))/(16 x^( 3/2) \[Theta] \[Kappa]^(3/2) (8 \[Theta] + 3 \[Kappa]))) + 
        1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]]) E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
          2 Sqrt[3])) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] -  Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$52039[2, 6, 1] +  1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]])
          E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] + Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$52039[2, 6,  2]) X2

I understand the reason of getting $ instead of numbers or mathematical expressions. It's because of the confusion between global and local variables. I changed the local variables but the $ still persists and defined the functions using Module command on my code. Please how to get read of the $ when computing the Lie bracket.

Also, the Lie bracket built-in command/ calculator from Wolfram Alpha (see link) is not functioning for symbolic computation. https://www.wolframalpha.com/input?i=%7B12%2C+20%7D+.+%7B16%2C+-5%7D