Extends Tanaka theory to supergeometry for upper bounds on supersymmetry.
problem Bounding supersymmetry dimensions of supergeometries.
method Extends Tanaka theory to supergeometry.
result Obtains an upper bound on supersymmetry dimensions.
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The paper realizes Lie superalgebras G(3) and F(4) as symmetries of supergeometries.
problem Addressing whether exceptional Lie superalgebras G(3) and F(4) are maximal symmetries of supergeometries.
method Considering negatively graded Lie superalgebras for every choice of parabolic subgroup, computing Tanaka-Weisfeiler prolongations, and reducing the structure group when required.
result Realization of 19 inequivalent G(3)-supergeometries and 55 inequivalent F(4)-supergeometries.
We realize the simple Lie superalgebra G(3) as supersymmetry of various geometric structures, most importantly super-versions of the Hilbert-Cartan equation (SHC) and Cartan's involutive PDE system that exhibit G(2) symmetry. We provide the symmetries explicitly and compute, via the first Spencer cohomology groups, the…
The paper realizes 6 supergeometries for the Lie superalgebra D(2,1;a).
problem Addressing the maximal supersymmetry of .
method Computing Tanaka-Weisfeiler prolongations for negatively graded Lie subalgebras.
result 6 inequivalent supergeometries realized for .