| Texto completo | |
| Autor(es): |
de Mello, Thiago Castilho
;
Souza, Manuela da Silva
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Linear Algebra and its Applications; v. 679, p. 15-pg., 2023-10-03. |
| Resumo | |
In this paper we study identities and images of polynomials on null-filiform Leibniz algebras. If L-n is an n-dimensional null-filiform Leibniz algebra, we exhibit a finite minimal basis for Id(L-n), the polynomial identities of L-n, and we explicitly compute the images of multihomogeneous polynomials on L-n. We present necessary and sufficient conditions for the image of a multihomogeneous polynomial f to be a subspace of L-n. For the particular case of multilinear polynomials, we prove that the image is always a vector space, showing that the analogue of the L'vov-Kaplansky conjecture holds for L-n. We also prove similar results for an analog of null-filiform Leibniz algebras in the infinite-dimensional case. (c) 2023 Elsevier Inc. All rights reserved. (AU) | |
| Processo FAPESP: | 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos |
| Beneficiário: | Ivan Chestakov |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |