Let $M$ is a smooth n-manifold and $g$ is a $Z\_2$-graded Lie algebra, we denote the algebra of smooth $g$-valued function on $M$ by $C^{\infty} (M,g)$. I wanna find all graded derivation of $C^{\infty} (M,g)$ and their relation to algebra of smooth function and smooth vector field on $M$. In the case of space-time manifold and special lie algebra this obtained some wonderful result. 
let me know Any reference related? 



Derivations of algebra of smooth $g$-valued function?
If $g$ is finite-dimensional, the algeba in question is isomorphic to $g \otimes C^\infty(M,\mathbb R)$. There is a full description of derivations of Lie algebras of the form $L \otimes A$ in terms of $L$ and $A$ (see, for example, arXiv:math/0302334, Corollary 2.2 and references therein). For example, if $L$ is perfect, centerless and central, then $Der(L\otimes A) \simeq (Der(L) \otimes A) \oplus Der(A)$.


