Special linear Lie algebra

Let be a field. is the Lie algebra realized by traceless matrices under their linear commutator. 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.

Gram matrix

Ordering the basis , we have the following Gram matrix

Properties

• Affine Lie algebras of sl_2

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