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Groupprops β

Derivation-invariance is Lie bracket-closed

Statement

Suppose L is a Lie ring and A,B are two derivation-invariant Lie subrings of L. Then, the subring:

[A,B] := \langle [a,b] \mid a \in A, b \in B \rangle

is a derivation-invariant subring. In other words, if d:L \to L is a derivation, then d[A,B] \le [A,B].

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Analogues