Let be a Lie algebra over a field of characteristic zero.
The Lie algebra of the compact form is 14 dimensional.
Thus the Lie algebra depends entirely on these intersection numbers.
But there are also just five "exceptional Lie algebras" that do not fall into any of these families.
This is simply a different, more convenient, representation of the same real Lie algebra.
These groups are all compact real forms of the same Lie algebra.
A set of all closed 1-forms, together with this bracket, form a Lie algebra.
The concept is also found in the theory of Lie algebras.
By simple connectivity the same is true at the level of Lie algebras.
Assume that g is a Lie algebra over a field of characteristic zero.
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