Take L to be a subspace of sl (2,R). (R is the real numbers)(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

L = \left(

\begin{array}{ccc}

0 & -c & b\\

c & 0 & -a\\

-b & a & 0

\end{array}\right)

[/tex]

The basis elements of L are

[tex]

e_1 = \left(

\begin{array}{ccc}

0 & 0 & 0\\

0 & 0 & -1\\

0 & 1 & 0

\end{array}\right)

[/tex]

[tex]

e_2 = \left(

\begin{array}{ccc}

0 & 0 & 1\\

0 & 0 & 0\\

-1 & 0 & 0

\end{array}\right)

[/tex]

[tex]

e_3 = \left(

\begin{array}{ccc}

0 & -1 & 0\\

1 & 0 & 0\\

0 & 0 & 0

\end{array}\right)

[/tex]

What is the best way to show that this Lie Algebra is simple (i.e. the only ideals are {0} and L? I know it's non-abelian.

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# Lie Algebra's question

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