The symmetry superalgebra of the super Hilbert-Cartan equation (1.7) and of the G(3)-contact super-PDE (1.8) is exactly the exceptional Lie superalgebra G(3).
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G(3)-supergeometry and a supersymmetric extension of the Hilbert-Cartan equation
The symmetry superalgebra of the super Hilbert-Cartan equation (1.7) and of the G(3)-contact super-PDE (1.8) is exactly the exceptional Lie superalgebra G(3).