Talk:PlanetPhysics/Equivalent Representations of Groupoids

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%%% Primary Title: equivalent representations of groupoids
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%%% Filename: EquivalentRepresentationsOfGroupoids.tex
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\begin{document}

 \begin{definition} Two \htmladdnormallink{representations}{http://planetphysics.us/encyclopedia/CategoricalGroupRepresentation.html} of \htmladdnormallink{groupoids}{http://planetphysics.us/encyclopedia/GroupoidHomomorphism2.html} $(\mu_i, U_{\grp} * \H, L_i)$ , for $i=1,2$
are called \emph{equivalent} if $\mu_1 \sim \mu_2$, and if there also exists a fiber-preserving
\htmladdnormallink{isomorphism}{http://planetphysics.us/encyclopedia/IsomorphicObjectsUnderAnIsomorphism.html} of analytical Hilbert space bundles $v: (U_{\grp}* \H_1)|_U \longrightarrow (U_{\grp}* \H_2)|_U$ ,
where $U$ is a measurable subset of $U_{\grp}$ of null complementarity; the isomorphism $v$
also has the following property:
$\hat{v}[r(x)]\hat{L}_1(x) = \hat{L}_2 \hat{v}[d(x)]$ for $x \in \grp |_U $.
\end{definition}

\end{document}
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