Graded vector space Degree operator Let be an -Graded vector space over where is a submonoid of the additive group. Then the degree operator is defined by linalg for any and . On a graded algebra If is an -Graded algebra over where is a submonoid of the additive group, the degree operator is a derivation, falg called the degree derivation. Proof Note that for homogenous elements and we have so by linearity is a derivation. In the case is a -graded Lie algebra, see adjoining the degree derivation. Properties Let be a linear map between -graded vector spaces over where is ^graded iff is ^homogenous of degree iff Proof proof tidy | en | sembr