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29 March 2024
 
  » arxiv » 0912.2933

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Periodicity of Adams operations on the Green ring of a finite group
R. M. Bryant ; Marianne Johnson ;
Date 15 Dec 2009
AbstractThe Adams operations $psi_Lambda^n$ and $psi_S^n$ on the Green ring of a group $G$ over a field $K$ provide a framework for the study of the exterior powers and symmetric powers of $KG$-modules. When $G$ is finite and $K$ has prime characteristic $p$ we show that $psi_Lambda^n$ and $psi_S^n$ are periodic in $n$ if and only if the Sylow $p$-subgroups of $G$ are cyclic. In the case where $G$ is a cyclic $p$-group we find the minimum periods and use recent work of Symonds to express $psi_S^n$ in terms of $psi_Lambda^n$.
Source arXiv, 0912.2933
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