GammaEquivariant 2003-08-21 17:32:47 2007-06-24 16:13:37 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here Let $\Gamma$ be a compact Lie group acting linearly on $V$ and let $g$ be a mapping defined as $g\colon V \to V$. Then $g$ is \emph{$\Gamma$-equivariant} if $$g(\gamma v)=\gamma g(v)$$ for all $\gamma \in \Gamma$, and all $v \in V$.\\ Therefore if $g$ commutes with $\Gamma$ then $g$ is $\Gamma$-equivariant. \cite{1} \begin{thebibliography}{1} \bibitem[GSS]{1} Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David.: Singularities and Groups in Bifurcation Theory \textit{(Volume II)}. Springer-Verlag, New York, 1988. \end{thebibliography}