Examples
Examples of semisimple Lie algebras, with notation coming from classification by Dynkin diagrams, are:
- , the special linear Lie algebra.
- , the odd-dimensional special orthogonal Lie algebra.
- , the symplectic Lie algebra.
- , the even-dimensional special orthogonal Lie algebra.
These Lie algebras are numbered so that n is the rank. Except certain exceptions in low dimensions, many of these are simple Lie algebras, which are a fortiori semisimple. These four families, together with five exceptions (E6, E7, E8, F4, and G2), are in fact the only simple Lie algebras over the complex numbers.
Read more about this topic: Semisimple Lie Algebra
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