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.