Calculating adjoint representation of a matrix Lie group

[Saumya biswas]

Dear all,

Is there a way of calculating the adjoint representation of a matrix Lie group in sage?

Specifically, can we calculate linear maps like 

for vectors X of the Lie Algebra? The notation is from

https://en.wikipedia.org/wiki/Baker%E2%80%93Campbell%E2%80%93Hausdorff_formula#An_important_lemma_and_its_application_to_a_special_case_of_the_Baker%E2%80%93Campbell%E2%80%93Hausdorff_formula

Please direct me in the right direction, if I posted in the wrong place/formatting.

Saumya