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