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
Famous quotes containing the word examples:
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)