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, #m/def/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 . #m/thm/lie

Proof

#missing/proof

#state/tidy | #lang/en | #SemBr