精确无发散向量场的李代数的通用中心扩展

arXiv - MATH - Differential Geometry Pub Date : 2024-09-08 DOI:arxiv-2409.05182

Bas Janssens, Leonid Ryvkin, Cornelia Vizman

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摘要

我们构建了精确无发散向量场的李代数的普遍中心扩展，证明了克劳德-罗杰（Claude Roger）在 1995 年提出的一个猜想。作为应用，我们构建了紧凑三维流形的精确无发散衍射的（无限维）李群的普遍中心扩展。

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Universal central extension of the Lie algebra of exact divergence-free vector fields

We construct the universal central extension of the Lie algebra of exact divergence-free vector fields, proving a conjecture by Claude Roger from 1995. The proof relies on the analysis of a Leibniz algebra that underlies these vector fields. As an application, we construct the universal central extension of the (infinite-dimensional) Lie group of exact divergence-free diffeomorphisms of a compact 3-dimensional manifold.

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arXiv - MATH - Differential Geometry

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