Graded derivation

A graded derivation is a generalization of a derivation on an algebra. Let $(𝐴, \cdot)$ be a graded algebra over $𝕂$ . A degree $𝑝$ graded derivation is a ^homogenous linear endomorphism $𝐷 : 𝐴 \to 𝐴$ satisfying the generalized product rule falg

𝐷 (𝑎 \cdot 𝑏) = 𝐷 (𝑎) \cdot 𝑏 + (- 1) 𝑝 𝑞 𝑎 \cdot 𝐷 (𝑏)

for homogenous $𝑎 \in 𝐴$ of degree $𝑞$ .