Let L be a Lie algebra. If L has a nondegenerate Killing form, then (over some algebraic extension of the ground field) L is the direct sum of absolutely simple Lie algebras. These Lie algebras have been classified and the classes are named A_n, B_n, C_n, D_n, E_6, E_7, E_8, F_4 and G_2. This function returns a single string containing the types of the direct summands of L.

> L := SimpleLieAlgebra("D", 7, RationalField());
> L;
Lie Algebra of dimension 91 with base ring Rational Field
> K := Centralizer(L, sub<L | [L.1,L.2,L.3,L.4]>);
> K;
Lie Algebra of dimension 41 with base ring Rational Field
> _,S := HasLeviSubalgebra(K);
> S;
Lie Algebra of dimension 6 with base ring Rational Field
> SemiSimpleType(S);
A1 A1