Classical Lie algebras

The classical Lie algebras are finite-dimensional Lie algebras over a field which can be classified into four types formula_1, formula_2, formula_3 and formula_4, where for formula_5 the general linear Lie algebra and formula_6 the formula_7 identity matrix:
Except for the low-dimensional cases formula_12 and formula_13, the classical Lie algebras are simple.
The Moyal algebra is an infinite-dimensional Lie algebra that contains all classical Lie algebras as subalgebras.