Imagens de polinômios multilineares sobre algumas subálgebras de matrizes

• Ano de defesa: 2019
• Autor(a) principal: Fagundes, Pedro Souza [UNIFESP]
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Paulo (UNIFESP)
• Palavras-chave em Português: Lvov-Kaplansky Conjecture; Multilinear Polynomials; Upper Triangular Matrices; Strictly Upper Triangular Matrices; Conjectura De Lvov-Kaplansky; Polinômios Multilineares; Matrizes Triangulares Superiores; Matrizes Estritamente Triangulares Superiores
• Link de acesso: https://sucupira.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=8319439; https://repositorio.unifesp.br/handle/11600/59487

In this dissertation we will study the images of multilinear polynomials on matrix algebras. We will present results from Shoda, Albert and Muckenhoupt, Mesyan and Buzinski and Winstanley to study the cases where the multilinear polynomials have degree up to four. We will also describe the images of multilinear polynomials of degree up to four on the upper triangular matrix algebra as well as the images of multilinear polynomials of arbitrary degree on the strictly upper triangular matrix algebra. Moreover, we will study some results from Brešar and Klep about the relation between the linear span of the images of noncommutative polynomials on algebras and Lie ideals.