Take a real semisimple Lie algebra, $\frak g$ with Iwasawa decomposition $\frak g = k \oplus a \oplus n$. Let $\mathfrak m :=Z_\frak k(a)$ be the centralizer in $\frak k$ of $\frak a$. I take it from some things I've read that $\frak m \oplus a \oplus n$ is solvable. This is clear to me except for the bracket of $\frak m$ with itself. It seems like it reduces to $\frak m$ being solvable. Why is $\frak m$ solvable?
2026-05-15 08:18:23.1778833103
Why is $\frak m$ solvable?
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