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PI-equivalência em álgebras graduadas simples
(Universidade Federal de São Carlos, 2016-02-29)
This work aims to give a description, under certain hypothesis, of the graded simple algebras and prove that they are determined by their graded identities. For this, we study the papers [3] and [19]. More precisely we ...
Estudo de nova fórmula de caracteres para representações de Álgebra de Lie semissimples
(Universidade Federal de São Carlos, 2015-08-28)
The objective of this dissertation is descrive formally the irreducible representations of finitedimensional semisimple Lie algebras g over a field F algebraically closed with characteristic zero, as also get some multiplicity ...
Um estudo de valorizações transcendentes e algébricas via polinômios-chaves e pares minimais
(Universidade Federal de São Carlos, 2022-02-24)
The main goal of this work is to study transcendental valuations and algebraic valuations. To achieve this, we use some of the main objects in Valuation Theory, such as key polynomials, truncations and minimal pairs. These ...
Identidades Polinomiais ℤ2-Graduadas para as Álgebras M1,1(E) e UT2(F) via representações de grupos
(Universidade Federal de São Carlos, 2017-09-01)
In this essay we will briefly study the concept of Algebra. We will introduce a little of Group Representation Theory, looking specifically at Young's Theory, which allows us to present explicitly the decomposition of the ...
Álgebras de Hopf, objetos galois e identidades polinomiais
(Universidade Federal de São Carlos, 2018-02-21)
Our main goal is to study Hopf algebras and Galois objects, from the point of view of
the polynomial identities, more precisely how these objects are distinguished by their
polynomial H-identities. To this end we follow ...
Sobre a metrizabilidade do espaço de R-lugares de um corpo de funções F com trdeg_R=1
(Universidade Federal de São Carlos, 2020-02-28)
The main purpose of this work is to study the metrizability of the space of R-places of a function field, with transcendence degree 1 over a real closed field. Specifically, we are going to present a necessary and sufficient ...
Symmetric and non-symmetric Jack Functions
(Universidade Federal de São Carlos, 2020-05-29)
The goal of this dissertation is to present the theory of Jack functions from the standpoint of algebraic combinatorics. The presentation of symmetric functions is largely centred on the first chapter of MacDonald's ...