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arXiv · 2406.03149

On crossed modules of pre-Lie algebras

Xuedan Luo
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Abstract

Given a Lie algebra $\mathfrak g$ and a $\mathfrak{g}$-module $V$, it is due to Gerstenhaber that there is an isomorphism between $H^3(\mathfrak{g}, V )$ and the group of equivalence classes of crossed modules with kernel $V$ and cokernel $\mathfrak {g}$. The goal of this article is to obtain this result for pre-Lie algebras and their modules.

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Xuedan Luo. 2024-06-05. On crossed modules of pre-Lie algebras. https://arxiv.org/abs/2406.03149

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