Abstract
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 ) = s l ( 1 | n ) can be constructed by adding a "gray" node to the Dynkin diagram of A n − 1 = s l ( 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.