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:

    “I wage not any feud with Death
    For changes wrought on form and face;
    No lower life that earth’s embrace
    May breed with him can fright my faith.”
    —Alfred Tennyson (1809–1892)