Let be a field. is the Lie algebra realized by traceless matrices under their linear commutator. #m/def/lie It has the Chevalley basis

with the commutation relations

where we have the nondegenerate invariant symmetric bilinear form

given by the Trace form of the fundamental representation, making a quadratic Lie algebra.

Properties

• Affine Lie algebras of

#state/develop | #lang/en | #SemBr