# Homology of solvable Lie algebras

Let $$\mathfrak{g}$$ be a solvable lie algebra and $$\lambda\in (\mathfrak{g}/[\mathfrak{g},\mathfrak{g}])^*$$ be the character of $$\mathfrak{g}$$. How to compute homology for $$\mathbb{C}_\lambda$$, the simple $$\mathfrak{g}-$$module with character $$\lambda$$?

I have faced strange behavior of homology, while calculating them manually for 2 and 3-dimensional algebras and cannot solve it in full generality. Thanks in advance!