Abstract

Graphs generalizing Cayley graphs and arising from various actions of groups on themselves are studied. A relationship between such graphs and subalgebras of operators in a group ring is established, which permits one to obtain a formula for the number of ends of such graphs in terms of the dimensions of appropriate character spaces. Examples of group actions and the corresponding graphs are constructed. In particular, under the action by conjugation, the corresponding algebra turns out to be an algebra of derivations. The proposed construction is generalized to Fox derivatives.

中文翻译：

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群代数和群端中的微分计算

摘要

研究了凯莱图的概括以及由群体对自身的各种行为产生的图。建立了此类图与群环中算子的子代数之间的关系，这允许人们根据适当的字符空间的维数获得此类图的端数的公式。构建了群体行动的示例和相应的图表。特别是，在共轭作用下，相应的代数变成了导数代数。所提出的结构可推广到 Fox 衍生品。