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The homology groups of some two-step nilpotent Lie algebras associated to symplectic vector spaces

E. Getzler
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Abstract

Let H be a symplectic vector space, let V be a vector space, and consider the nilpotent Lie algebra L_H(V) = H \otimes V + S^2(V) with bracket [(h_1 \otimes v_1;a_1),(h_2 \otimes v_2;a_2)] = (0, v_1 v_2) . In this paper, we calculate the Lie algebra homology of L_H(V) as a polynomial functor of V. This has applications to the analysis of the Leray-Serre spectral sequence of the fibrations of moduli spaces of pointed curves M_{1,n}->M_{1,1} and M_{g,n}->M_g.

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E. Getzler. 1999-03-24. The homology groups of some two-step nilpotent Lie algebras associated to symplectic vector spaces. https://arxiv.org/abs/math/9903147

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