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

Root system

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.

C-series

B-series

D-series

Notes

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

This article is issued from Wikiversity. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.