论部分群作用的同源性

Emmanuel Jerez
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引用次数: 0

摘要

我们用简单的方法研究部分群作用的部分群(共)同调。我们引入了 $K$ 模块上部分群作用的普适全局化概念,并证明给定 $G$ 在 $M$ 上的部分表示,部分群同调 $H^{par}_{\bullet}(G,M)$ 自然地与通常的群同调 $H_{\bullet}(G, KG\otimes_{G_{par}} M)$ 同构,其中 $KG \otimes_{G_{par}} 是与 $M$ 相关的部分群作用的普适全局化。M$ 是与 $M$ 相关的部分群作用的通用全局化。我们将这一结果对偶化为收敛于$H^{\bullet}_{par}(G,M)$的同调谱序列。
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On the homology of partial group actions
We study the partial group (co)homology of partial group actions using simplicial methods. We introduce the concept of universal globalization of a partial group action on a $K$-module and prove that, given a partial representation of $G$ on $M$, the partial group homology $H^{par}_{\bullet}(G, M)$ is naturally isomorphic to the usual group homology $H_{\bullet}(G, KG \otimes_{G_{par}} M)$, where $KG \otimes_{G_{par}} M$ is the universal globalization of the partial group action associated to $M$. We dualize this result into a cohomological spectral sequence converging to $H^{\bullet}_{par}(G,M)$.
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