Print Email Facebook Twitter Classification of finite-dimensional modules over semisimple Lie algebras Title Classification of finite-dimensional modules over semisimple Lie algebras Author Liu, Jin Jun (TU Delft Electrical Engineering, Mathematics and Computer Science) Contributor Groenevelt, W.G.M. (mentor) Wagenaar, C.C.M.L. (mentor) Versendaal, R. (graduation committee) Degree granting institution Delft University of Technology Programme Applied Mathematics Date 2023-07-13 Abstract Sophus Lie (1842-1899) known as the founder of the theory of transformation groups, originally aimed to study solutions of differential equations via their symmetries. Over the decades this theory has evolved into the theory of Lie groups. These Lie groups are of an analytic and geometric nature, but Sophus Lie's principal discovery was that these groups can be studied by their "infinitessimal generators" leading to a linearization of the group. The group structure endows this linearized space with a special bracket operation, [x,y]=xy-yx, which gives rise to Lie algebras.The main applications for Lie algebras stem from physics, notably in quantum mechanics and particle physics. It turns out that representations of Lie algebras are the way to describe symmetries of physical systems. So, it becomes an important task to figure out what all the possible representations are. Thus, our main goal for this thesis is to classify all finite-dimensional semisimple Lie algebra representations. Subject Representation TheoryLie AlgebraUniversal Enveloping AlgebrasPBW TheoremRoot SystemVerma modules To reference this document use: http://resolver.tudelft.nl/uuid:bc81a1c4-44ea-4dcb-99ac-2143c13c8430 Part of collection Student theses Document type bachelor thesis Rights © 2023 Jin Jun Liu Files PDF BSc_Thesis_Lie_Algebra_ji ... junliu.pdf 628.46 KB Close viewer /islandora/object/uuid:bc81a1c4-44ea-4dcb-99ac-2143c13c8430/datastream/OBJ/view