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