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 #m/def/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, #m/thm/falg called the degree 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

1. is graded iff
2. is homogenous of degree iff

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