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Linear Algebraic Groups

CIT4130018Elective Modules9 ECTSEnglishUnregelmäßigDepartment Mathematics
AI-edited module sheet. Based on the TUMonline module description, edited for readability.Original in TUMonline

What it is about

You will learn the theory of linear algebraic groups: structure, core concepts and central structural results such as connected components, Lie algebras, quotients and Jordan decomposition. In the end you will be able to apply these results and analyze examples as well as transfer the concepts to connections with representation theory, arithmetic geometry and invariant theory.

What you will be able to do

  • Characterization of linear algebraic groups
  • Analysis of connected components and Lie algebras
  • Understanding of quotients and Jordan decomposition
  • Distinction and use of solvable and reductive groups
  • Application of the most important results to examples

What the module consists of

  • VorlesungConveying theoretical foundations and examples (blackboard lecture)
  • ÜbungDiscussion of problems that deepen and illustrate lecture topics

Teaching method

  • Tafelvortragfor the presentation of theoretical principles and examples
  • Übungsblätter/Übungssitzungenfor the deeper understanding and application of the lecture content
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Official page in TUMonline · Details are not binding.