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author | Andreas Müller <andreas.mueller@ost.ch> | 2021-04-11 10:30:05 +0200 |
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committer | Andreas Müller <andreas.mueller@ost.ch> | 2021-04-11 10:30:05 +0200 |
commit | 15881729aa3f1293d546a1692a02094ed3f24e2b (patch) | |
tree | 7a051091d6f507ad3ab28dbd227206ad1288f368 /vorlesungen/slides/7/liealgebra.tex | |
parent | phasen (diff) | |
download | SeminarMatrizen-15881729aa3f1293d546a1692a02094ed3f24e2b.tar.gz SeminarMatrizen-15881729aa3f1293d546a1692a02094ed3f24e2b.zip |
phases
Diffstat (limited to '')
-rw-r--r-- | vorlesungen/slides/7/liealgebra.tex | 27 |
1 files changed, 22 insertions, 5 deletions
diff --git a/vorlesungen/slides/7/liealgebra.tex b/vorlesungen/slides/7/liealgebra.tex index 892216e..574467b 100644 --- a/vorlesungen/slides/7/liealgebra.tex +++ b/vorlesungen/slides/7/liealgebra.tex @@ -8,50 +8,64 @@ \setlength{\abovedisplayskip}{5pt} \setlength{\belowdisplayskip}{5pt} \frametitle{Lie-Algebra} +\ifthenelse{\boolean{presentation}}{\vspace{-15pt}}{\vspace{-8pt}} \begin{block}{Vektorraum} Tangentialvektoren im Punkt $I$: \begin{center} \begin{tabular}{>{$}c<{$}|p{6cm}|>{$}c<{$}} \text{Lie-Gruppe $G$}&Tangentialvektoren&\text{Lie-Algebra $LG$} \\ \hline +\uncover<2->{ \operatorname{GL}_n(\mathbb{R}) & beliebige Matrizen & M_n(\mathbb{R}) +} \\ +\uncover<3->{ \operatorname{O(n)} & antisymmetrische Matrizen & \operatorname{o}(n) +} \\ +\uncover<4->{ \operatorname{SL}_n(\mathbb{R}) & spurlose Matrizen & \operatorname{sl}_2(\mathbb{R}) +} \\ +\uncover<5->{ \operatorname{U(n)} & antihermitesche Matrizen & \operatorname{u}(n) +} \\ +\uncover<6->{ \operatorname{SU(n)} & spurlose, antihermitesche Matrizen & \operatorname{su}(n) +} \end{tabular} \end{center} \end{block} \vspace{-20pt} \begin{columns}[t,onlytextwidth] \begin{column}{0.40\textwidth} +\uncover<7->{% \begin{block}{Lie-Klammer} Kommutator: $[A,B] = AB-BA$ -\end{block} +\end{block}} +\uncover<8->{% \begin{block}{Nachprüfen} $[A,B]\in LG$ für $A,B\in LG$ -\end{block} +\end{block}} \end{column} \begin{column}{0.56\textwidth} +\uncover<9->{% \begin{block}{Algebraische Eigenschaften} \begin{itemize} -\item antisymmetrisch: $[A,B]=-[B,A]$ -\item Jacobi-Identität +\item<10-> antisymmetrisch: $[A,B]=-[B,A]$ +\item<11-> Jacobi-Identität \[ [A,[B,C]]+ [B,[C,A]]+ @@ -59,9 +73,12 @@ für $A,B\in LG$ = 0 \] \end{itemize} +\vspace{-13pt} +\uncover<12->{% {\usebeamercolor[fg]{title} Beispiel:} $\mathbb{R}^3$ mit Vektorprodukt $\mathstrut = \operatorname{so}(3)$ -\end{block} +} +\end{block}} \end{column} \end{columns} \end{frame} |