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Group Cohomology and
${{L}^{p}}$-Cohomology of Finitely Generated Groups
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- Journal:
- Canadian Mathematical Bulletin / Volume 46 / Issue 2 / 01 June 2003
- Published online by Cambridge University Press:
- 20 November 2018, pp. 268-276
- Print publication:
- 01 June 2003
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- Article
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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.
