|Unit level:||Level 6|
|Teaching period(s):||Semester 2|
|Offered by||School of Mathematics|
|Available as a free choice unit?:||N
To introduce the students to the basics of algebraic groups and to study and the Lie algebra of an algebraic group and quotients in more detail.
The study of algebraic groups is a fascinating mixture of groups and algebraic geometry and ia a very active field of research. In this course the students will meet the familiar themes of irreducibility, connectedness and dimension from algebraic geometry. In the ase of algebraic groups these concepts behave particulary nicely. The students will also study actions of algebraic groups and an essential theorem about how algebraic groups can be embedded in general linear groups. The second half of the course will be a more detailed look at Lie algebras of algebraic groups and quotients. Various important theorems will be proved about and using these two important concepts. Many examples will be given throughout the course to aid with the students' understanding.
- Other - 20%
- Written exam - 80%
Assessment Further Information
Coursework: weighted 20%
End of semester examination: three hours weighting 80%
Revision on Algebraic Geometry and definition and examples of Algebraic Groups 
Irreducibility, Connectedness and Dimension 
Actions of Algebraic Groups 
Linear Algebraic Groups 
Lie Algebra of an Algebraic Group 
Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding. Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback. Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.
- Assessment practical exam - 50 hours
- Lectures - 22 hours
- Tutorials - 11 hours
- Independent study hours - 67 hours