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The Type of a Semisimple Lie Algebra
The Type of a Semisimple Lie Algebra
SemiSimpleType(L) : AlgLie -> AlgLie
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.
Example AlgLie_SemiSimpleType (H49E8)
We compute the semisimple type of the Levi subalgebra of the simple
Lie algebra of type D_7.
> 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
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