I stumbled across this statement and I have trouble solving it.
Let L be a non-abelian 2-dimensional Lie algebra. Then the centre of L is trivial, meaning Z(L)=0.
How can one solve this?
2026-04-06 13:09:40.1775480980
centre of a non-abelian 2-dimensional Lie algebra
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If it's non-Abelian then it's spanned by two elements $a$ and $b$ with $[a,b]\ne0$. Can you show that for any non-zero $c\in L$ that either $[a,c]\ne0$ or $[b,c]\ne0$?