The exact sequence $0\rightarrow sl(A)\rightarrow gl(A)\rightarrow A/[A,A]\rightarrow 0$ gives rise to a spectral sequence in homology, I want to know the details for this spectral sequence at the second page?



Spectral sequence in Lie algebra
This is explained in the article of Beno Eckmann and Urs Stammbach "On exact sequences in the homology of groups and algebras". The Hochschild-Serre spectral sequence for homology of Lie algebras, applied to the short exact sequence $0\rightarrow N \rightarrow G \rightarrow Q \rightarrow 0$ of Lie algebras, and every $Q$-module $M$ yields long exact sequences in homology, see $(I)$ to $(VIII)$ in Eckmann's and Stammbach's paper: $(I)$ is $H\_2(G,M)\rightarrow H\_2(Q,M)\rightarrow \cdots H\_1(G,M)\rightarrow H\_1(Q,M)\rightarrow 0$, $(VIII)$ is $H\_n(G,M)\rightarrow H\_n(Q,M)\rightarrow H\_{n-2}(Q,H\_1(N,M))\rightarrow \cdots \rightarrow H\_1(Q,M)\rightarrow 0$. 


