Hi @erou, how are you?

I am working with left-invariant involutive structures on compact Lie groups. It has a fancy description. Still, it is just the study of solvability and regularity of linear systems of partial differential equations. These linear systems have some nice algebraic symmetries inherited from the Lie group. If you are curious about it, you can ask questions or even take a look at my thesis: https://teses.usp.br/teses/disponiveis/45/45132/tde-25032019-092801/publico/Thesis_Dissertation___Final_version.pdf

Symbolic computation is fantastic! Can you be a little more specific on the problem you are working on?