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