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.

dkrashen@uga.edu

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