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Fixed an overful hbox.
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cionx committed Apr 8, 2019
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Expand Up @@ -515,7 +515,7 @@ \subsubsection{Split Extensions and Semidirect Products}
We therefore find that the commutator~$[(x,0), (y,0)]$ is again contained in~$\hlie \oplus 0$ for all~$x, y \in \hlie$.
This means that~$\kappa = 0$.

The linear map~$\theta \colon \hlie \to I$ is given by taking for~$x \in \hlie$ the restriction of the endomorphism~$\ad_{\hlie \oplus I}((x,0))$ to the ideal~$0 \oplus I$ and then identifying~$0 \oplus I$ with~$I$ to get~$\theta(x) \in \Der(I)$.
The linear map~$\theta \colon \hlie \to I$ takes for~$x \in \hlie$ the restriction of the endomorphism~$\ad_{\hlie \oplus I}((x,0))$ to the ideal~$0 \oplus I$ and then identifying~$0 \oplus I$ with~$I$ to get~$\theta(x) \in \Der(I)$.
This assignment may be written as the composition
\[
\theta
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