Ado's theorem
= Ado's theorem
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= Ado theorem
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Every finite-dimensional <Lie algebra> over a <field> of <characteristic zero> has a finite-dimensional faithful <Lie algebra representation>. Thus it embeds as a Lie subalgebra of a <matrix algebra>, using the <matrix commutator> as bracket. Faithfulness is crucial for detecting central elements: the <Adjoint representation> alone kills the <center of a Lie algebra>.