IDENTITIES OF REPRESENTATIONS OF NILPOTENT LIE-ALGEBRAS

Let N be a nilpoteat of class 2 Lie algebra with one-dimensional centr e C = Kc over an infinite field K and let rho : N --> End(K)(V) be a r epresentation of N in a vector space V such that rho(c) is invertible in End(K)(V). We find a basis for the identities of the representation rho. As consequences we obtain a basis for all the weak polynomial id entities of the pair (M-2(K), sl(2)(K)) over an infinite field K of ch aracteristic 2 and describe the identities of the regular representati on of Lie algebras related with the Weyl algebra and its tensor powers .