Quasi-Frobenius Lie Algebra

In mathematics, a quasi-Frobenius Lie algebra

over a field is a Lie algebra

equipped with a nondegenerate skew-symmetric bilinear form

, which is a Lie algebra 2-cocycle of with values in . In other words,

for all, in .

If is a coboundary, which means that there exists a linear form such that

then

is called a Frobenius Lie algebra.

Read more about Quasi-Frobenius Lie Algebra:  Equivalence With Pre-Lie Algebras With Nondegenerate Invariant Skew-symmetric Bilinear Form

Famous quotes containing the words lie and/or algebra:

    “All that I have said and done,
    Now that I am old and ill,
    Turns into a question till
    I lie awake night after night
    And never get the answers right.”
    —William Butler Yeats (1865–1939)

    “Poetry has become the higher algebra of metaphors.”
    —José Ortega Y Gasset (1883–1955)