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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