Abstract
AbstractLetKbe any field of characteristic two and let$U_1$and$W_1$be the Lie algebras of the derivations of the algebra of Laurent polynomials$K[t,t^{-1}]$and of the polynomial ringK[t], respectively. The algebras$U_1$and$W_1$are equipped with natural$\mathbb{Z}$-gradings. In this paper, we provide bases for the graded identities of$U_1$and$W_1$, and we prove that they do not admit any finite basis.
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