Overview of Lie Groups and Their Lie Algebras

Detta är en Kandidat-uppsats från KTH/Skolan för teknikvetenskap (SCI)

Författare: Jonathan Krook; [2020]

Nyckelord: ;

Sammanfattning: Intuitively, Lie groups are groups that are also smooth. The aim of this thesis is to describe how Lie groups are defined as smooth manifolds, and to look into their properties. To each Lie group there exists an associated vector space, which is called the Lie algebra of the Lie group. We will investigate what properties of a Lie group can be derived from its Lie algebra. As an application, we will characterise all unitary irreducible finite dimensional representations of the Lie group SO(3).

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