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

TL;DR

The paper presents two explicit geometric realizations of the exceptional Lie superalgebra $F(4)$ as symmetry superalgebras of specific super-PDE systems of second and third order.

Contribution

It provides the first explicit geometric realizations of $F(4)$ as supersymmetries in super-PDE systems of different orders.

Findings

Realizations as symmetry superalgebras of second-order super-PDEs.

Realizations as symmetry superalgebras of third-order super-PDEs.

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.