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UBC Theses and Dissertations

Generations and relations for rings of invariants Askarogullari, Murat Can


In this thesis we first prove that the algebra of invariants for reductive groups over the base field complex numbers are finitely generated. Then we focus on invariant algebras of finite groups. After showing the natural relation between invariant algebras and reflections in the group we prove the Chevalley-Shephard-Todd theorem. We conclude with classification of complex finite reflection groups and some examples. Throughout the thesis we follow similar arguments as in Springer[8] and Kane[6] where we give full details on the arguments.

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