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 lakes are something which you are unprepared for; they lie up so high, exposed to the light, and the forest is diminished to a fine fringe on their edges, with here and there a blue mountain, like amethyst jewels set around some jewel of the first water,—so anterior, so superior, to all the changes that are to take place on their shores, even now civil and refined, and fair as they can ever be.”
—Henry David Thoreau (1817–1862)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)