 Quasi-Frobenius Lie algebra

In mathematics, a quasi-Frobenius Lie algebra 

over a field formula_2 is a Lie algebra 

equipped with a nondegenerate skew-symmetric bilinear form 

for all formula_8, formula_9, formula_10 in formula_5.If formula_12 is a coboundary, which means that there exists a linear form formula_13 such that
then
is called a Frobenius Lie algebra.