Identidades polinomiais para a álgebra de Jordan das matrizes triangulares superiores 2x2
Let K be a field (finite or infinite) of char(K) ≠ 2, and let UTn = UTn(K) be the n x n upper triangular matrix algebra over K. If · is the usual product on UTn, then with the new product a ○ b = (1/2)(a·b + b·a), UTn becomes a Jordan algebra, denoted by UJn = UJn(K). In this thesis, we describe the...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | Brasil |
| Institución: | Universidade Federal de São Carlos (UFSCAR) |
| Repositorio: | Repositório Institucional da UFSCAR |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufscar.br:20.500.14289/15149 |
| Acceso en línea: | https://repositorio.ufscar.br/handle/20.500.14289/15149 |
| Access Level: | acceso abierto |
| Palabra clave: | Ágebra das matrizes triangulares superiores Álgebra de Jordan Identidades polinomiais Álgebra graduada Identidades polinomiais graduadas Propriedade de Specht Upper triangular matrix algebra Jordan algebra Polynomial identities Graded algebra Graded polynomial identities Specht property CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA |
| Sumario: | Let K be a field (finite or infinite) of char(K) ≠ 2, and let UTn = UTn(K) be the n x n upper triangular matrix algebra over K. If · is the usual product on UTn, then with the new product a ○ b = (1/2)(a·b + b·a), UTn becomes a Jordan algebra, denoted by UJn = UJn(K). In this thesis, we describe the set I of all polynomial identities of UJ2 for any K, and we prove that I has the Specht property when K is infinite, namely that, I and every T-ideal containing I, is finitely generated as a T-ideal. Moreover, we describe the set of all Z2-graded polynomial identities of UJ2 with any Z2-grading, and we describe a linear basis for the corresponding relatively free Z2-graded algebra. |
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