Quasi-Frobenius Lie Algebra - Equivalence With Pre-Lie Algebras With Nondegenerate Invariant Skew-symmetric Bilinear Form

Equivalence With Pre-Lie Algebras With Nondegenerate Invariant Skew-symmetric Bilinear Form

If is a quasi-Frobenius Lie algebra, one can define on another bilinear product by the formula

.

Then one has and

is a pre-Lie algebra.

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