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Title: Algebraic groups and Tannakian categories
Author: Sala Fernandez, Guillem
Director/Tutor: Crespo Vicente, Teresa
Keywords: Grups algebraics diferencials
Treballs de fi de grau
Àlgebres de Hopf
Categories (Matemàtica)
Teoria de Galois
Differential algebraic groups
Bachelor's thesis
Hopf algebras
Categories (Mathematics)
Galois theory
Issue Date: 29-Jun-2017
Abstract: [en] The main goal of this memoir is to introduce the notion of an algebraic group and study its properties, generalizing many common notions in group theory, such as representations and actions. In addition, we see that there is a duality between affine algebraic groups and what we call Hopf algebras. Afterwards, we see that we can define a category whose objects are finite representations of affine algebraic groups together with the natural homomorphisms between them. This leads us to the necessity of introducing a more general structure for this kind of categories, which we call tannakian categories. Eventually, we apply the results we obtain with these structures to differential Galois theory.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Teresa Crespo Vicente
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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