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Type: Artigo de periódico
Title: Z-graded Identities Of The Lie Algebra W1
Author: Freitas J.A.
Koshlukov P.
Krasilnikov A.
Abstract: Let K be a field of characteristic 0 and let W1 be the Lie algebra of the derivations of the polynomial ring K[t]. 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.
Editor: Academic Press Inc.
Rights: fechado
Identifier DOI: 10.1016/j.jalgebra.2014.12.023
Date Issue: 2015
Appears in Collections:Unicamp - Artigos e Outros Documentos

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