Exercise 4, § 3

Tag 00VK, permanent. Cite it as [Bourbaki, Tag 00VK].

Lie Groups and Lie Algebras, VII, 58

Let = $(2,\mathbf{R}),x=(1$ 0 $), y=(0-1)$ . Show that $\mathbf{R}x$ and $\mathbf{R}y$

$\mathfrak{g}\mathfrak{s}\mathfrak{l}$ 0 $-1$ 1 0

are Cartan subalgebras of $\mathfrak{g}$ not conjugate under Aut( $\mathfrak{g}$ ).

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