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 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

References