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

الأصل · EN

Let H be a symplectic vector space, let V be a vector space, and consider the nilpotent Lie algebra Lₕ(V) = H ⊗ V + S²(V) with bracket [(h₁ ⊗ v₁;a₁),(h₂ ⊗ v₂;a₂)] = (0,<h₁,h₂> v₁ v₂). In this paper, we calculate the Lie algebra homology of Lₕ(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 M₁,ₙ->M₁,₁ and Mg,ₙ->Mg.