Z-graded identities of the Lie algebra W-1

Autor(es)

Freitas, Jose A. ^[1] ; Koshlukov, Plamen ^[2] ; Krasilnikov, Alexei ^[1]

Afiliação do(s) autor(es)

^[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF - Brazil

^[2] Univ Estadual Campinas, IMECC, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 427, p. 226-251, APR 1 2015.
• Citações Web of Science: 1

Resumo

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. (AU)

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