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:

    “The innocent are so few that two of them seldom meet—when they do meet, their victims lie strewn around.”
    —Elizabeth Bowen (1899–1973)

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