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Jun 3, 2019 at 8:28 comment added Simon Wadsley I don't think that the spectral stabilises until the third page: there can be (indeed given YCor's answer there are) non-zero maps $d\colon E^2_{i,0}\to E^2_{i-2,1}$.
Jun 3, 2019 at 6:37 comment added Boris Bilich You have also proved it in both directions, haven't you? Since $H_i(\mathfrak{g}/\mathfrak{z} , H_j(\mathfrak{z} ,\mathbb{C}_\lambda))\neq 0$ by induction and the spectral sequence stabilizes on the second sheet $H_{i+j}(\mathfrak{g},\mathbb{C}_\lambda)$ is also nonzero. I'm not sure, because it contradicts with YCor's answer, but I cannot find a mistake.
May 14, 2019 at 20:38 history edited Simon Wadsley CC BY-SA 4.0
Fixed minor typos.
May 10, 2019 at 17:15 comment added Simon Wadsley Of course this also addresses Victor Protsak's question on another answer.
May 10, 2019 at 17:09 history answered Simon Wadsley CC BY-SA 4.0