GAP (NoCK) - Chapter 1: Notation

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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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