# Isometries and quaternions

Lecturer: Ruben Tellechea Zamanillo

Date: 08/03/2017

Time: 17:00

Place: Room 103

Abstract: It is known that the complex numbers appeared as an extension of $\mathbb{R}$ to find solutions to equations such as $x ^ 2 + 1 = 0$ . The field $\mathbb{C}$ can be extended again to $\mathbb{H}$ by adding another imaginary unit $j$ such that $j^2 = -1$. $\mathbb{H}$ is (as $\mathbb{C}$) a real division algebra algebraically closed. With the product of quaternions we can represent the isometries in the real three-dimensional euclidean vector space (R3) easily. In this colloquium we will present some concepts to understand better these representations and their utilities.