# 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.

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## Bibliography

- Verónica Pericacho,
*Cuaterniones y octoniones* - Richard Palais,
*The classification of real division algebras* - Samuel Eilenberg and Ivan Niven,
*The “fundamental theorem of algebra” for quaternions*.