| Texto completo | |
| Autor(es): |
Fagundes, Pedro
Número total de Autores: 1
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| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Algebra; v. 644, p. 19-pg., 2024-02-01. |
| Resumo | |
Let F be an algebraically closed field of characteristic different from 2. We show that the images of multilinear (*)-graded polynomials on UT2 are homogeneous vector spaces. An analogous result holds for UT3 endowed with non-trivial grading. We further show that these results are optimal, in the following sense: there exist multilinear *-graded polynomials whose image on UTn (n >= 3) with the trivial grading is not a vector space, and whose image on UTn (n >= 4) with the natural Z(n)-grading is also not a vector space. In particular, an analog of the L'vov-Kaplansky conjecture can not be expected in the setting of algebras with (graded) involutions. (c) 2024 Elsevier Inc. All rights reserved. (AU) | |
| Processo FAPESP: | 22/05256-2 - Imagens de polinômios multilineares sobre UT_2 e UT_3 com involuções |
| Beneficiário: | Pedro Souza Fagundes |
| Modalidade de apoio: | Bolsas no Exterior - Estágio de Pesquisa - Doutorado |
| Processo FAPESP: | 19/16994-1 - Álgebras que são soma de duas subálgebras PI |
| Beneficiário: | Pedro Souza Fagundes |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado |