Defining Relations for the Exceptional Lie Superalgebras of Vector Fields

Abstract

We list defining relations for four of the five exceptional simple Lie superalgebras of vector fields with polynomial coefficients. This is done for one of many inequivalent systems of simple roots (generators). For the fifth superalgebra the result is not final: there might be infinitely many relations. On the contrary, for the same Lie super-algebra with Laurent polynomials as coefficients there are only finitely many relations. To show perspective, the complete list of simple complex vectorial Lie superalgebras is given, and their relations have been calculated (also for one system of generators only) in [GLP].