Title of the course: Quaternions
Instructor: Prof. Adrien Deloro
Institution: Sorbonne Université
Dates: 26 July – 7 August 2021
Prerequisites: Linear Algebra 2, Group Theory
Level: Advanced undergraduate
Abstract: Quaternions were discovered less than 200 years ago by Irish mathematician Hamilton. They almost form a field, where one can add, subtract, multiply and divide, but where a.b fails to be b.a.
One can investigate quaternions from a variety of points of view: linear algebra, basic representation theory, group theory, Lie theory… they even have applications in number theory.
I’ll try to explain all this. The focus will be on algebraic structures, so it is necessary to have good familiarity with say, n by n matrices over the reals and the complex numbers.
Language: EN