Explicit generators of $\mathfrak{so}(6)$

Question

I'm looking for a canonical way to write the matrix form of the $\mathfrak{so}(6)$ generators, either in printed or digital form or implemented in some programming language represented in arbitrary dimension.

Answer 1

You can program the basis and the Lie brackets of $\mathfrak{so}(6)$ yourself. Take the vector space of all $6\times 6$ skew-symmetric matrices, and chose a basis $X_1,\ldots ,X_{15}$. Then the Lie brackets are just given by the rule $$ [X_i,X_j]=X_iX_j-X_jX_i. $$