Group Cohomology and $L^p$-Cohomology of Finitely Generated Groups

[摘要] Let $G$ be a finitely generated, infinite group, let $p>1$, and let$L^p(G)$ denote the Banach space ${ sum_{xin G} a_xx mid sum_{xinG} |a_x |^p < infty }$. In this paper we will study the firstcohomology group of $G$ with coefficients in $L^p(G)$, and the firstreduced $L^p$-cohomology space of $G$. Most of our results will be for aclass of groups that contains all finitely generated, infinite nilpotentgroups.

[学科分类] 数学（综合）

[关键词] group cohomology;$L^p$-cohomology;central element of infinite order;harmonic function;continuous linear functional