Abstract
We give an analog of a Chevalley-Serre presentation for the Lie superalgebras and of Cartan type. These are part of a wider class of Lie superalgebras, the so-called tensor hierarchy algebras, denoted and , where denotes the Kac-Moody algebra Ar, Dr or Er. Then W(An−1) and S(An−1) are the Lie superalgebras and . The algebras and are constructed from the Dynkin diagram of the Borcherds-Kac-Moody superalgebras obtained by adding a single grey node (representing an odd null root) to the Dynkin diagram of . We redefine the algebras W(Ar) and S(Ar) in terms of Chevalley generators and defining relations. We prove that all relations follow from the defining ones at level . The analogous definitions of the algebras in the D- and E-series are given. In the latter case the full set of defining relations is conjectured.