From 1fb743df08b0734932d510c6b11405d0a2dbbe47 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sat, 10 Apr 2021 19:57:13 +0200
Subject: new slides

---
 vorlesungen/slides/7/liealgebra.tex | 69 +++++++++++++++++++++++++++++++++++++
 1 file changed, 69 insertions(+)
 create mode 100644 vorlesungen/slides/7/liealgebra.tex

(limited to 'vorlesungen/slides/7/liealgebra.tex')

diff --git a/vorlesungen/slides/7/liealgebra.tex b/vorlesungen/slides/7/liealgebra.tex
new file mode 100644
index 0000000..16a7aa0
--- /dev/null
+++ b/vorlesungen/slides/7/liealgebra.tex
@@ -0,0 +1,69 @@
+%
+% liealgebra.tex -- Lie-Algebra
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Lie-Algebra}
+\vspace{-20pt}
+\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
+\operatorname{GL}_n(\mathbb{R})
+& beliebige Matrizen
+& M_n(\mathbb{R})
+\\
+\operatorname{O(n)}
+& antisymmetrische Matrizen
+& \operatorname{o}(n)
+\\
+\operatorname{SL}_n(\mathbb{R})
+& spurlose Matrizen
+& \operatorname{sl}_2(\mathbb{R})
+\\
+\operatorname{U(n)}
+& antihermitesche Matrizen
+& \operatorname{u}(n)
+\\
+\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}
+\begin{block}{Lie-Klammer}
+Kommutator: $[A,B] = AB-BA$
+\end{block}
+\begin{block}{Nachprüfen}
+$[A,B]\in LG$
+für $A,B\in LG$
+\end{block}
+\end{column}
+\begin{column}{0.56\textwidth}
+\begin{block}{Algebraische Eigenschaften}
+\begin{itemize}
+\item antisymmetrisch: $[A,B]=-[B,A]$
+\item Jacobi-Identität
+\[
+[A,[B,C]]+
+[B,[C,A]]+
+[C,[A,B]]
+= 0
+\]
+\end{itemize}
+{\usebeamercolor[fg]{title}
+Beispiel:} $\mathbb{R}^3$ mit Vektorprodukt $\mathstrut = \operatorname{so}(3)$
+\end{block}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1


From 4d96632a4cb5dce985c92bc5daebe272dcbc1410 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sat, 10 Apr 2021 23:01:39 +0200
Subject: typos

---
 vorlesungen/slides/7/liealgebra.tex | 1 -
 1 file changed, 1 deletion(-)

(limited to 'vorlesungen/slides/7/liealgebra.tex')

diff --git a/vorlesungen/slides/7/liealgebra.tex b/vorlesungen/slides/7/liealgebra.tex
index 16a7aa0..892216e 100644
--- a/vorlesungen/slides/7/liealgebra.tex
+++ b/vorlesungen/slides/7/liealgebra.tex
@@ -8,7 +8,6 @@
 \setlength{\abovedisplayskip}{5pt}
 \setlength{\belowdisplayskip}{5pt}
 \frametitle{Lie-Algebra}
-\vspace{-20pt}
 \begin{block}{Vektorraum}
 Tangentialvektoren im Punkt $I$:
 \begin{center}
-- 
cgit v1.2.1


From 15881729aa3f1293d546a1692a02094ed3f24e2b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 11 Apr 2021 10:30:05 +0200
Subject: phases

---
 vorlesungen/slides/7/liealgebra.tex | 27 ++++++++++++++++++++++-----
 1 file changed, 22 insertions(+), 5 deletions(-)

(limited to 'vorlesungen/slides/7/liealgebra.tex')

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}
-- 
cgit v1.2.1

