On crossed modules of pre-Lie algebras

Fuente: arXiv
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Main Author: Luo, Xuedan
Format: Preprint
Published: 2024
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author Luo, Xuedan
author_facet Luo, Xuedan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_03149
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On crossed modules of pre-Lie algebras
Luo, Xuedan
Representation Theory
Rings and Algebras
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.
title On crossed modules of pre-Lie algebras
topic Representation Theory
Rings and Algebras
url https://arxiv.org/abs/2406.03149