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.
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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.
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The classical Lie algebras are ...... l Lie algebras as subalgebras.
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The classical Lie algebras are ...... l Lie algebras as subalgebras.
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Classical Lie algebras
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