Crespo Vicente, TeresaSala Fernandez, Guillem2018-05-162018-05-162017-06-29https://hdl.handle.net/2445/122398Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Teresa Crespo Vicente[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.81 p.application/pdfengcc-by-nc-nd (c) Guillem Sala Fernandez, 2017http://creativecommons.org/licenses/by-nc-nd/3.0/esGrups algebraics diferencialsTreballs de fi de grauÀlgebres de HopfCategories (Matemàtica)HomeomorfismesTeoria de GaloisDifferential algebraic groupsBachelor's thesesHopf algebrasCategories (Mathematics)HomeomorphismsGalois theoryinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess