The classical Lie algebras are finite-dimensional Lie algebras over a field which can be classified into four types , , and , where for the general linear Lie algebra and the identity matrix:
, the special linear Lie algebra; , the odd orthogonal Lie algebra; , the symplectic Lie algebra; and , the even orthogonal Lie algebra.
Except for the low-dimensional cases and , the classical Lie algebras are simple.
The Moyal algebra is an infinite-dimensional Lie algebra that contains all classical Lie algebras as subalgebras.
See also Simple Lie algebra Classical group
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