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:

    “The principle of majority rule is the mildest form in which the force of numbers can be exercised. It is a pacific substitute for civil war in which the opposing armies are counted and the victory is awarded to the larger before any blood is shed. Except in the sacred tests of democracy and in the incantations of the orators, we hardly take the trouble to pretend that the rule of the majority is not at bottom a rule of force.”
    —Walter Lippmann (1889–1974)