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:

    “Even as fog continues to lie in the valleys, so does ancient sin cling to the low places, the depressions in the world consciousness.”
    —Dewitt Bodeen (1908–1988)

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