We consider finite-dimensional complex semi-simple Lie algebras g. Any such Lie algebra has a Cartan subalgebra h, and its adjoint representation on g yields a root space decomposition of g, which in turn gives rise to a root system. These are in turn classified by the Dynkin diagrams. Conversely, for any root system, there is a corresponding semi-simple Lie algebra, and the complex semi-simple Lie algebras are therefore classified by the root system. Given a root system, Serre’s theorem states explicitly how to reconstruct corresponding semi-simple Lie algebra from this root system.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-488524 |
| Date | January 2022 |
| Creators | Gustavsson, Bim |
| Publisher | Uppsala universitet, Algebra, logik och representationsteori |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | U.U.D.M. project report ; 2022:38 |
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