| Texto completo | |
| Autor(es): |
Fideles, Claudemir
;
Koshlukov, Plamen
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | RECENT PROGRESS IN RING AND FACTORIZATION THEORY; v. 477, p. 24-pg., 2025-01-01. |
| Resumo | |
Let K be an infinite field and let W-1 and U-1 be the Lie algebras of the derivations of the algebras of polynomials K[t] and of Laurent polynomials K[t, t(-1)], respectively. The algebras W-1 and U-1 admit natural Z-gradings. We provide a basis for the graded identities of W-1 and of U-1 and prove that they do not admit any finite basis. Additionally, we provide a basis for the identities of certain graded Lie algebras with a grading such that every homogeneous component has dimension <= 1, assuming that a basis of the multilinear graded identities is known. The Z-graded identities for W-1, in characteristic 0, were described in the paper [10]; we give an alternate and characteristic-free proof of the main theorem of [10]. It should be noted that our results hold also in characteristic 2, although the proofs are rather different than those when the characteristic of K is different from 2. We also describe the graded identities of the Virasoro algebras assuming K is of characteristic different from 2 and 3. Furthermore, the methods developed here make it possible to describe bases of the graded identities for certain graded algebras equipped with a grading known as fine. For instance, the special linear Lie algebra sl(q) (K) with the Pauli gradings, where q is a prime, can be considered. (AU) | |
| Processo FAPESP: | 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos |
| Beneficiário: | Ivan Chestakov |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 23/04011-9 - Estrutura de álgebra graduadas e/ou com traço, e teoria dos Invariantes |
| Beneficiário: | Claudemir Fideles Bezerra Júnior |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |