Classical Lie algebras

The classical Lie algebras are finite-dimensional Lie algebras over a field which can be classified into four types

n

{\displaystyle {\mathfrak {gl}}(n)}

the general linear Lie algebra and

identity matrix: Except for the low-dimensional cases

, the classical Lie algebras are simple.

[1][2] The Moyal algebra is an infinite-dimensional Lie algebra that contains all classical Lie algebras as subalgebras.