Quasi-Frobenius Lie algebra

In mathematics, a quasi-Frobenius Lie algebra

:

over a field $k$ is a Lie algebra :$(mathfrak\{g\},\; [,,,,,,,]\; )$

equipped with a nondegenerate skew-symmetric bilinear form

:, which is a Lie algebra 2-cocycle of $mathfrak\{g\}$ with values in $k$. In other words,

::

for all $X$, $Y$, $Z$ in $mathfrak\{g\}$.

ee also

*Lie coalgebra
*Lie bialgebra
*Lie algebra cohomology

References

* Jacobson, Nathan, "Lie algebras", Republication of the 1962 original. Dover Publications, Inc., New York, 1979. ISBN 0-486-63832-4
* Vyjayanthi Chari and Andrew Pressley, "A Guide to Quantum Groups", (1994), Cambridge University Press, Cambridge ISBN 0-521-55884-0.