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Concept
Quasi-Frobenius Lie algebra
Summary
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.
If is a quasi-Frobenius Lie algebra, one can define on another bilinear product by the formula
Then one has
and
is a pre-Lie algebra.
Official source
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