Generators and relations for (generalised) Cartan type superalgebras
Paper in proceedings, 2018
In Kac's classification of finite-dimensional Lie superalgebras, the contragredient ones can be constructed from Dynkin diagrams similar to those of the simple finite-dimensional Lie algebras, but with additional types of nodes. For example, A(n−1,0)=sl(1|n) can be constructed by adding a "gray" node to the Dynkin diagram of An−1=sl(n), corresponding to an odd null root. The Cartan superalgebras constitute a different class, where the simplest example is W(n), the derivation algebra of the Grassmann algebra on n generators. Here we present a novel construction of W(n), from the same Dynkin diagram as A(n−1,0), but with additional generators and relations.