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One can use the .to_word_list() method on a monomial in PBW basis.


sage: PBW[-alpha[1]-alpha[2]]*PBW[-alpha[1]].to_word_list()
>>>>  [-alpha[1]-alpha[2],-alpha[1]]

The resulting list of roots are keys in the basis of the original Lie algebra, and can hence be easily converted. This solves my problem.