部分群表示的同调研究
代数拓扑
2025-10-16 v2 群论
K理论与同调
摘要
我们研究了具有部分表示M中群G的部分群（co）同调如何可使用常规群（co）同调来描述。为此，我们引入了部分群表示M的通用全球化Lambda(M)的概念。我们的主要结果表明，部分群同调H^{par}_*(G,M)自然等同于经典群同调H_*(G,Lambda(M))。我们将此结果扩展到上同调框架，得到一个涉及经典群上同调的谱序列，其收敛于部分群上同调。值得注意的是，当G可数时，谱序列会塌缩， resulting in a natural isomorphism H^{*}_{par}(G,M)cong H^{*}(G,Hom_{K_{par}G}(Lambda(K_{par}G),M))，其中K_{par}G代表G的部分群代数。
引用
@article{arxiv.2404.14650,
title = {On the homology of partial group representations},
author = {Emmanuel Jerez},
journal= {arXiv preprint arXiv:2404.14650},
year = {2025}
}
备注
This version is a more compact version of the previous one, focusing primarily on partial representations of groups and omitting sections on the homology of partial actions. This change aims to make the structure of the paper more concise and centered on addressing the main problem. The title has been updated accordingly. Minor typographical errors were also corrected