Graduações e identidades polinomiais graduadas para a álgebra de matrizes triangulares superiores
Let F be a field and let G be a group. Denote by UTn(F) the algebra of n × n upper triangular matrices over F. The mathematicians Valenti and Zaicev described all G-gradings on UTn(F), and the mathematicians Di Vincenzo, Koshlukov and Valenti described the set of all G-graded polynomial identities o...
| Author: | |
|---|---|
| Format: | master thesis |
| Status: | Published version |
| Publication Date: | 2020 |
| Country: | Brasil |
| Institution: | Universidade Federal de São Carlos (UFSCAR) |
| Repository: | Repositório Institucional da UFSCAR |
| Language: | Portuguese |
| OAI Identifier: | oai:repositorio.ufscar.br:20.500.14289/13568 |
| Online Access: | https://repositorio.ufscar.br/handle/20.500.14289/13568 |
| Access Level: | Open access |
| Keyword: | Álgebra Graduações Identidades polinomiais graduadas Álgebra de matrizes triangulares superiores Algebra Gradings Graded polynomial identities Algebra of upper triangular matrices CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA::GRUPOS DE ALGEBRA NAO-COMUTAVIVA |
| Summary: | Let F be a field and let G be a group. Denote by UTn(F) the algebra of n × n upper triangular matrices over F. The mathematicians Valenti and Zaicev described all G-gradings on UTn(F), and the mathematicians Di Vincenzo, Koshlukov and Valenti described the set of all G-graded polynomial identities of UTn(F) when F is an infinite field. After, Koshlukov and Yukihide described the elementary G-gradings on the Lie algebra UTn(F)^(−). In this dissertation, we study these results. Moreover, Koshlukov and Yukihide described the Zn-graded polynomial identities of the Lie algebra UTn(F)^(−) when the grading is canonical and F has characteristic 0. In this dissertation, we give another proof of this fact. |
|---|