A Lie conformal superalgebra and duality of representations for E(4,4)

We construct a duality functor in the category of continuous representations of the Lie superalgebra E(4, 4), the only exceptional simple linearly compact Lie superalgebra, for which it wasn't known. This is achieved by constructing a Lie conformal superalgebra of type (4, 4) for which E(4, 4) is the annihilation algebra. Along the way we obtain an explicit realization of E(4, 4) by vector fields on a (4|4)-dimensional supermanifold.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we construct a duality functor in the category of continuous representations to study the Lie superalgebra E(4, 4). By constructing a specific type of Lie conformal superalgebra, we obtain that E(4, 4) is its annihilation algebra. Furthermore, we also obtain an explicit realization of E(4, 4) on a supermanifold in the process of studying.