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Type: Artigo de periódico
Title: Z-graded Identities Of The Lie Algebra W-1
Author: Freitas
Jose A.; Koshlukov
Plamen; Krasilnikov
Abstract: Let K be a field of characteristic 0 and let W-1 be the Lie algebra of the derivations of the polynomial ring K[t]. The algebra W-1 admits a natural Z-grading. We describe the graded identities of W-1 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 W-1 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. (c) 2015 Elsevier Inc. All rights reserved.
Subject: Polynomial-identities
Country: SAN DIEGO
Citation: Z-graded Identities Of The Lie Algebra W-1. Academic Press Inc Elsevier Science, v. 427, p. 226-251 APR-2015.
Rights: embargo
Identifier DOI: 10.1016/j.jalgebra.2014.12.023
Date Issue: 2015
Appears in Collections:Unicamp - Artigos e Outros Documentos

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