Degree operator Adjoining the degree derivation Let be a -Graded Lie algebra over with a submonoid, so that we may define the degree derivation . Then by adjoining the derivation to one gets a unique graded structure on such that is the degree operator, lie whence . Modules Let be a -Graded Lie algebra over with a submonoid and be a graded module* over . Then is also a graded module over where acts as the Degree operator on , i.e. for . lie Proof proof tidy | en | sembr