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 for all

β

is a coboundary, which means that there exists a linear form

such that then is called a Frobenius Lie algebra.

] , β )

is a quasi-Frobenius Lie algebra, one can define on

another bilinear product

and is a pre-Lie algebra.