论文标题
通过部分组代数的同源和同源学
Homology and cohomology via the partial group algebra
论文作者
论文摘要
我们通过局部群体代数$ \ mathbb {k} _ {par} g $从环理论的角度研究部分同源性和共同体。特别是，我们将组$ g $的部分同源性和共同体与不可约（不可约合的）$ \ mathbb {k} _ {par} g $ - 模块与普通同源性和$ g $的普通同源性和同胞组中的系数联系起来。此外，我们比较标准的共同学维度$ cd_ {\ \ \ \ \ \ \ \ \ \ \ \ {k}}（g）$（在字段$ \ mathbb {k} $上，与部分共同体学维度$ cd_ {\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \米\ \ Mathbb {k}}^{par}（g）\ geq cd_ {\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \）$，并且对于$ g = \ mathbb {z} $有相等的态度。
We study partial homology and cohomology from ring theoretic point of view via the partial group algebra $\mathbb{K}_{par}G$. In particular, we link the partial homology and cohomology of a group $G$ with coefficients in an irreducible (resp. indecomposable) $\mathbb{K}_{par}G$-module with the ordinary homology and cohomology groups of $G$ with in general non-trivial coefficients. Furthermore, we compare the standard cohomological dimension $cd_{ \ \mathbb{K}}(G)$ (over a field $\mathbb{K}$) with the partial cohomological dimension $cd_{ \ \mathbb{K}}^{par}(G)$ (over $\mathbb{K}$) and show that $cd_{ \ \mathbb{K}}^{par}(G) \geq cd_{ \ \mathbb{K}}(G)$ and that there is equality for $G = \mathbb{Z}$.
