Central Simple Algebras

UGA MATH 8330, Spring 2015. An introduction to the theory of finite dimensional division algebras, the Brauer group, involutions and other fun things.


Lecture 1: Wedderburn-Artin Theory
Lecture 2: Tensors and Centralizers
Lecture 3: Noether-Skolem and examples
Lecture 4: Crossed Products
Lecture 5: Second and first cohomology groups
Lecture 6: Cohomology and the connecting map
Lecture 7: Primary decomposition and some involutions
Lecture 8: Involutions and other anti-automorphisms
Lecture 9: Existence of involutions and division algebras
Lecture 10: Cayley-Hamilton and friends
Lecture 11: Ramification, introduction
Lecture 12: Ramification, part 2