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|Type:||Artigo de periódico|
|Title:||Z-graded Identities Of The Lie Algebra W1|
|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.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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