The five exceptional simple Lie superalgebras of vector fields and their fourteen regradings

Abstract

The five simple exceptional complex Lie superalgebras of vector fields are described. One of them, f a s \mathfrak {fas} , is new; the other four are explicitly described for the first time. All nonisomorphic maximal subalgebras of finite codimension of these Lie superalgebras, i.e., all other realizations of these Lie superalgebras as Lie superalgebras of vector fields, are also described; there are 14 of them altogether. All of the exceptional Lie superalgebras are obtained with the help of the Cartan prolongation or a generalized prolongation.