| Texto completo | |
| Autor(es): |
Fideles, Claudemir
;
Koshlukov, Plamen
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Algebra; v. 633, p. 28-pg., 2023-07-25. |
| Resumo | |
Let K be an infinite field of characteristic different from two and let U1 be the Lie algebra of the derivations of the algebra of Laurent polynomials K[t, t-1]. The algebra U1 admits a natural Z-grading. We provide a basis for the graded identities of U1 and prove that they do not admit any finite basis. Moreover, we provide a basis for the identities of certain graded Lie algebras with a grading such that every homogeneous component has dimension & LE; 1, if a basis of the multilinear graded identities is known. As a consequence of this latter result we are able to provide a basis of the graded identities of the Lie algebra W1 of the derivations of the polynomial ring K[t]. The Z-graded identities for W1, in characteristic 0, were described in [8]. As a consequence of our results, we give an alternative proof of the main result, Theorem 1, in [8], and generalize it to positive characteristic. We also describe a basis of the graded identities for the special linear Lie algebra slq(K) with the Pauli gradings where q is a prime number. (AU) | |
| Processo FAPESP: | 19/12498-0 - Identidades polinomiais graduadas e com traço, e teoria dos invariantes |
| Beneficiário: | Claudemir Fideles Bezerra Júnior |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |
| Processo FAPESP: | 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos |
| Beneficiário: | Ivan Chestakov |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |