# 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

edit### Root system

edit### Realisation

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

An A-series Lie algebra is realised by the ring of n-by-n traceless matrices.

## C-series

edit## B-series

edit## D-series

edit## Notes

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