The abelianization of the special derivation Lie algebra of free Lie algebras contains infinitely many linearly independent elements and non-trivial elements killed by Morita traces.
Satoh; On the basis-conjugating automorphism groups of free groups and free metabelian groups, Math
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On the abelianization of the special derivation Lie algebras of free Lie algebras
The abelianization of the special derivation Lie algebra of free Lie algebras contains infinitely many linearly independent elements and non-trivial elements killed by Morita traces.