Abstract
Let (L,N) be a pair of Lie algebras, in which N is an ideal of L. We prove if dim(N)=n and dim(L/N)=m, then the dimension of the second relative homology of (L,N) is equal to 12n(n+2m−1)−t, for some non-negative integer t. Also, we characterize all pairs of nilpotent Lie algebras for which t=0,1,2,3.
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