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

Puls, Michael J.

Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 268-276

Résumé

Let $G$ be a finitely generated, infinite group, let $p\,>\,1$ , and let ${{L}^{p}}\left( G \right)$ denote the Banach space $\left\{ \sum{_{x\in G}{{a}_{x}}x}|\sum{_{x\in G}|{{a}_{x}}{{|}^{p}}<\infty } \right\}$ . In this paper we will study the first cohomology group of $G$ with coefficients in ${{L}^{p}}\left( G \right)$ , and the first reduced ${{L}^{p}}$ -cohomology space of $G$ . Most of our results will be for a class of groups that contains all finitely generated, infinite nilpotent groups.

Détail

DOI : 10.4153/CMB-2003-027-x

Mots-clés : 43A15, 20F65, 20F18, group cohomology, Lp -cohomology, central element of infinite order, harmonic function, continuous linear functional