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

Published online by Cambridge University Press:  20 November 2018

Michael J. Puls
Michael J. Puls*
Affiliation:
Department of Mathematics, Eastern Oregon University, One University Boulevard, La Grande, OR 97850, USA, e-mail: [email protected]
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Abstract

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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.

Keywords

43A1520F6520F18group cohomologyLp-cohomologycentral element of infinite orderharmonic functioncontinuous linear functional
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 2 , 01 June 2003 , pp. 268 - 276
Copyright
Copyright © Canadian Mathematical Society 2003

References

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