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.

Read more about this topic:  Quasi-Frobenius Lie Algebra

Famous quotes containing the word form:

    “Others form man; I tell of him, and portray a particular one, very ill-formed, whom I should really make very different from what he is if I had to fashion him over again. But now it is done.”
    —Michel de Montaigne (1533–1592)