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

1999/03/24 by Ezra Getzler, E. Getzler, Getzler, E. · 1 citation
Mathematics · #17B30 #17B55 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AT #math.KT #msc:17B30 #msc:17B55

paper · pdf · doi:10.48550/arxiv.math/9903147

10 pages

arxiv created 1999/03/24 · openalex publication_date 1999/03/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a symplectic vector space, let V be a vector space, and consider the nilpotent Lie algebra L_H(V) = H ⊗ V + S²(V) with bracket [(h₁ ⊗ v₁;a₁),(h₂ ⊗ v₂;a₂)] = (0, v₁ v₂) . 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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• On the Homology of Nilpotent k-ary Lie Algebras

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