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Freitas, José A.; Koshlukov, Plamen; Krasilnikov, Alexei
Journal of algebra, 04/2015, Letnik: 427Journal Article
Let K be a field of characteristic 0 and let W1 be the Lie algebra of the derivations of the polynomial ring Kt. The algebra W1 admits a natural Z-grading. We describe the graded identities of W1 for this grading. It turns out that all these Z-graded identities are consequences of a collection of polynomials of degree 1, 2 and 3 and that they do not admit a finite basis. Recall that the “ordinary” (non-graded) identities of W1 coincide with the identities of the Lie algebra of the vector fields on the line and it is a long-standing open problem to find a basis for these identities. We hope that our paper might be a step to solving this problem.
