4 hours of lectures and exercises per week.
Lecturer
Jesper Funch Thomsen
Content
From linear algebra we know that the set of invertible linear maps on a finite dimensional vector space form a group. In this course we will study such groups and their (Zariski) closed subgroups called linear algebraic groups. We will regard linear algebraic groups as algebraic varieties and we therefore start the course with a brief introduction to algebraic geometry. Following this we turn to the study of linear algebraic groups starting with the commutative, nilpotent and solvable ones. This leads us to the Jordan decomposition and to the classification of the linear algebraic groups of dimension 1. We end the course by describing and defining the Lie algebra of a linear algebraic group.
Prerequisites
Algebra 2. Some familiarity with algebraic geometry either through the course "Commutative algebra" (E02) or in combination with "Algebraic geometry" (F03), described elsewhere in this book, will be helpful.
Literature
T. Springer, Linear algebraic groups, Birkhäuser, second edition 1998.
Evaluation
Students who do not intend to take a degree in Mathematics or Statistics from the University of Aarhus, but wish to earn credits for a 2.dels course from the Department of Mathematics, should indicate at the beginning of the course that they wish to be examined.
The form of examination for these students will be active participation together with oral or written contributions.
Credits
10 ECTS
Semester
Spring 2003