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...

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Detalles Bibliográficos
Autor: Ferreira, Lorrayne Cristina Silva
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2020
País:Brasil
Institución:Universidade Federal de São Carlos (UFSCAR)
Repositorio:Repositório Institucional da UFSCAR
Idioma:portugués
OAI Identifier:oai:repositorio.ufscar.br:20.500.14289/13568
Acceso en línea:https://repositorio.ufscar.br/handle/20.500.14289/13568
Access Level:acceso abierto
Palabra clave: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
Descripción
Sumario: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.