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Cartan Subalgebra

Cartan Subalgebra

CartanSubalgebra(L) : AlgLie -> AlgLie
Given a Lie algebra L, return a Cartan subalgebra of L. The algorithm works for Lie algebras L defined over a field F such that |F| > dim L and for restricted Lie algebras of characteristic p. If the Lie algebra does not fit into one of these classes then the correctness of the output is not guaranteed.

Example AlgLie_CartanSubalgebra (H49E4)

We compute a Cartan subalgebra of the simple Lie algebra of type A_4 over the rational field.

> L := SimpleLieAlgebra("F", 4, RationalField());
> L;
Lie Algebra of dimension 52 with base ring Rational Field
> H := CartanSubalgebra(L);
Lie Algebra of dimension 4 with base ring Rational Field
> H*H;
Lie Algebra of dimension 0 with base ring Rational Field
> Normalizer(L, H);
Lie Algebra of dimension 4 with base ring Rational Field

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