Linear Lie algebras

A linear (or "classical") Lie algebras is a Lie algebra whose elements can be represented as matrices (or linear transformations over some vector space over a field.

## A-series

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### Root system

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### Realisation

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See also: sl(n) (special linear Lie algebra)

An A-series Lie algebra  A n {\displaystyle A_{n}} is realised by the ring of n-by-n traceless matrices.

## C-series

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## B-series

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## D-series

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## Notes

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* James E. Humphreys (1972), Introduction to Lie Algebras and Representation Theory, Springer-Verlag, ISBN 9780387900537