What is the Cartan's subalgebra of set $D_{0 (n)}$ which consists of n x n matrices with diagonal null?
I'm trying the case, $n=2$ and $n=3$, but I'm not coming to any conclusion,for $n=2$ $X= X^T; X\in D_{0(2)}$ ok, in the case 3x3 is not ok.
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1Sorry, I do not understand what you are asking. Are looking for Cartan subalgebras of a certain Lie algebra? But what Lie algebra? The square matrices with diagonal $0$ do not form a Lie algebra in general ($[\pmatrix{0&1\0&0},\pmatrix{0&0\1&0}]=$?). – Torsten Schoeneberg Apr 08 '21 at 00:40
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It's true, the exercise was wrong!!! – Tiago Perdigão Apr 08 '21 at 18:44