Classical Lie algebras

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-dimensional orthogonal Lie algebra; * , the symplectic Lie algebra; and * , the even-dimensional 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.

Classical Lie algebras

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-dimensional orthogonal Lie algebra; * , the symplectic Lie algebra; and * , the even-dimensional 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.