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memoria.pdf (432.64 KB)

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Bachelor thesis

Publication date

2017-06-29

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cc-by-nc-nd (c) Guillem Sala Fernandez, 2017
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/122398

Algebraic groups and Tannakian categories

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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.

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Teresa Crespo Vicente

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Grups algebraics diferencials, Treballs de fi de grau, Àlgebres de Hopf, Categories (Matemàtica), Homeomorfismes, Teoria de Galois

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Differential algebraic groups, Bachelor's theses, Hopf algebras, Categories (Mathematics), Homeomorphisms, Galois theory

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Treballs Finals de Grau (TFG) - Matemàtiques

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SALA FERNANDEZ, Guillem. Algebraic groups and Tannakian categories. [consulted: 7 of June of 2026]. Available at: https://hdl.handle.net/2445/122398

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