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1 Notation

1 Notation

We use the notation and convention for real Lie algebras as is from CoReLG Package, [DFdG14].

gap> G:=RealFormById( "E", 7,3);

<Lie algebra of dimension 133 over SqrtField>
gap> rankG:=Dimension(CartanSubalgebra(G));

7
gap> rankRG:=Dimension(CartanSubspace(G));

3
gap> dimG:=Dimension(G);

133
gap> P:=CartanDecomposition( G ).P;

<vector space over SqrtField, with 54 generators>
gap> dimPforG:=Dimension(P);

54
gap> K:=CartanDecomposition( G ).K;

<Lie algebra of dimension 79 over SqrtField>
gap> rankK:= Dimension(CartanSubalgebra(K));

7
gap> dimK:= Dimension(K);

79

Classification can be found in Table 9 in [OV90], p. 312-317.

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