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

Realisation

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

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

Notes

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