ADE Classification - Lie Algebras

Lie Algebras

In terms of complex semisimple Lie algebras:

• corresponds to the special linear Lie algebra of traceless operators,
• corresponds to the even special orthogonal Lie algebra of even dimensional skew-symmetric operators, and
• are three of the five exceptional Lie algebras.

In terms of compact Lie algebras and corresponding simply laced Lie groups:

• corresponds to the algebra of the special unitary group
• corresponds to the algebra of the even projective special orthogonal group, while
• are three of five exceptional compact Lie algebras.