I read in mark wildon book "introduction to lie algebras"(adsbygoogle = window.adsbygoogle || []).push({});

"Let F be any field. Up to isomorphism there is a unique two-dimensional nonabelian

Lie algebra over F. This Lie algebra has a basis {x, y} such that its Lie

bracket is described by [x, y] = x"

and i'm curious,

How can i proof with this bracket [x,y] = x, satisfies axioms of Lie algebra such that

[a,a] = 0 for $a \in L$

and satisfies jacoby identity

cause we only know about bracket of basis vector for L

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# Two Dimensional Lie Algebra

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