Cartan subalgebra

In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra ${\displaystyle {\mathfrak {h}}}$ of a Lie algebra ${\displaystyle {\mathfrak {g}}}$ that is self-normalising (if ${\displaystyle [X,Y]\in {\mathfrak {h}}}$ for all ${\displaystyle X\in {\mathfrak {h}}}$, then ${\displaystyle Y\in {\mathfrak {h}}}$). They were introduced by Élie Cartan in his doctoral thesis.

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