Let $\mathfrak{g}$ be a Lie algebra over a field $K$. Then the Lie algebra cohomology of $\mathfrak{g}$ with coefficients in $V$ is the right derived functor of $V\mapsto V^\mathfrak{g}$ and can be described by Ext functor: $H^*(\mathfrak{g},V) \cong \mathrm{Ext}^*_{U(\mathfrak{g})}(K, V)$.
My question: I know that $H^*(\mathfrak{g},V)=\bigoplus_{i}H^i(\mathfrak{g},V)$. What is about $\mathrm{Ext}^*_{U(\mathfrak{g})}(K, V)$? Does $\mathrm{Ext}^*_{U(\mathfrak{g})}(K, V)=\bigoplus_{i}\mathrm{Ext}^i_{U(\mathfrak{g})}(K, V)$?