Exceptionally simple super-PDE for $F(4)$

Abstract

For the largest exceptional simple Lie superalgebra $F(4)$, having dimension $(24|16)$, we provide two explicit geometric realizations as supersymmetries, namely as the symmetry superalgebra of super-PDE systems of second and third order respectively.

34 pages, v3: acknowledgments completed. Final version to appear on Commun. Contemp. Math

References in corpus (4)

• Exceptionally simple PDE
• Irreducible complex skew-Berger algebras
• New relations between $G_2$-geometries in dimensions 5 and 7
• Lowest degree invariant 2nd order PDEs over rational homogeneous contact manifolds